I.1What is PostHarvestPro?

It is a postharvest physiology and technology program that runs in the browser, with nothing to install. It brings together in one place the computations that accompany a fruit or vegetable from harvest to the consumer, and it explains every result in words and says which method and which source it comes from.

It computes quality and maturity indices and color in CIELAB with its differences; it fits the kinetics of deterioration and predicts shelf life at one temperature or at any, including the time to rejection with fruit still sound when the trial ends; it measures respiration and ethylene, recognizes the climacteric and designs modified atmospheres, precooling and its heat load; it quantifies the losses of a chain in kilograms and in money, and mechanical damage; it analyzes discrimination, affective and descriptive sensory evaluation and designs the tastings; it analyzes postharvest trials with destructive sampling or with the same fruit over time; it solves the packaging, storage and transport calculations; and, at the end, it assembles a report with handling recommendations.

It is intended for teaching and research in postharvest, for quality control in packinghouses and marketers, and for anyone who advises growers. Everything is computed with engines written from scratch for this program, without other people’s libraries, and every method cites the work that defines it: on the app’s home page, at the foot of every result and in the methods of the report.

I.2The questions it answers

A good way to find out whether the program is for you is to see which questions it answers, and in which block.

I.3Six ideas that hold up the manual

Everything that follows rests on six ideas. If you keep them in mind, many of the mistakes made when analyzing postharvest data are no longer possible.

1. Temperature rules. Almost all deterioration speeds up with temperature, and not in a straight line: with a typical activation energy, each extra 10 °C multiplies the rate by three or four. That is why Chapter 3 does not stop at “the lot lasted 10 days”: it takes the constants to Arrhenius and predicts the life at the storage temperature.
2. The reaction order is chosen on the original scale. Linearizing a curve and comparing R² values changes the scale of the error and misleads. The app fits the three orders by nonlinear least squares and compares them by their AIC.
3. A fruit still sound at the end is not lost data. If the trial ends before every fruit is rejected, the survivors are censored: they contribute information while they were under observation. Discarding them shortens the estimated life.
4. A loss is measured in kilograms and in money. What is lost at the start of the chain weighs more; what is lost at the end is worth more. The best investment is not always where the most kilograms are lost.
5. The unit of analysis is the one that was randomized. If different fruit are sampled each day, the trial is a factorial; if the same fruit are weighed every day, it is a repeated-measures trial and its p-values must be corrected. In a tasting, each consumer is a block.
6. A model summarizes what was measured; it does not replace it. Predictions outside the temperatures, times or cultivars measured are extrapolations, and the app says so when it happens. The tables of permeabilities, size grades and compatibility are a guide only: use those of your film, your standard and your cultivar.

I.4What data it accepts and what it delivers

Every tool that analyzes a table has the same data input: Load example, Open file (CSV, TXT, XLSX, ODS), Paste a table or dropping the file on the box. Then the app proposes which column plays each role—time, group, attribute, consumer, product…—by its name, and you confirm or change the proposal. The direct-computation tools (the laboratory calculators, temperature, modified atmosphere, all of Block 8) are filled in by typing in their fields or in editable tables, where + Add row adds a line and × removes it.

I.5What you need and how to open it

Only a modern browser, in a version from the last few years, on a computer, a tablet or a phone. There is nothing to install and no internet is needed; the whole program fits in one folder.

1. Double-click index.html. It is the simplest way and everything works the same: the computations and the ten example data sets are inside the program.
2. Or double-click Open PostHarvestPro.bat. It starts a minimal local server on port 9970 and opens the app at http://localhost:9970. You only need it to open the app from another computer or a tablet on the same network; the server.ps1 file explains how.
3. Or online, at the app’s address in the LABG Suite, once it is published.

Your preferences—the language, the light or dark theme and the last tab you opened in each block—are kept in the browser itself and remembered next time. The data are not: every time you open the app it starts empty. To resume a piece of work there is the .json project of Block 9, which saves the tables you loaded, the columns you chose, the edited tables and the settings, and recomputes everything when you open it. If you try to close the tab after having worked, the app warns you.

This manual opens from the app itself: the User’s manual link is at the foot of its home page (Block 1); with the interface in Spanish, the link leads to the Spanish edition.

I.6A tour of the interface

All the applications of the suite share the same bar, the same navigation and the same figure tools, so what you learn here also serves you in the others.

1 2 3 4 5 6 7 8 9 10 11 12

• 1Name of the app and its motto. The name leads to the home page (Block 1).
• 2LABG Suite. Goes back to the portal with the other applications.
• 3ES · EN. Changes the language of the whole interface, including that of the figures and of the report.
• 4Theme, animations, report and help. The sun switches between the light and the dark theme; the sparkles button turns animations off or on; the speech bubble opens “Report a problem”; the question mark, the list of shortcuts (key ?).
• 5The bar of the nine blocks. The number turns into a check mark when the block already has a result, and the count at the top says how many there are (1/9 in the figure).
• 6The path. The app, the block, the tab and the card you are in.
• 7Document · Focused. All the cards of the block one after another, or one at a time; the button next to it collapses or expands them all.
• 8Search (Ctrl + K). A block, a section, a control or a figure, by its name.
• 9In this block. The tabs of the open block and, inside the current one, its cards; the one you are viewing is highlighted.
• 10The block title, with its number and what it does in one line.
• 11The tabs. Each block divides its tools into tabs; the app remembers the last one you opened in each.
• 12The data input. The example data set with its description and its SIMULATED tag, the buttons to load it or open your file and, below, the column for each role.

Getting around without getting lost

At the foot of each block two buttons lead to the previous and the next one. When you change a control and the results are recomputed further down, a floating button appears that takes you back to the control you touched, and another to go back to the top. Results are redone by themselves: when you change a setting, instantly; when you load new data—an example, a file, a pasted table or another column—the analysis runs inside the suite’s waiting screen, which only appears, with the message Analyzing the data…, if it takes more than a moment. Almost everything can also be done from the keyboard:

Every result is explained

Below each analysis there are three things besides the figures and the tables: some tiles with the numbers that matter (the chosen order, the life to the limit, the p-value), a reading in words of what they mean for the product, and the line Method and source: with the method and the citation. When something calls for care—an extrapolation, a straight line with a low R², a time that not all treatments have—a warning says so in the same place.

The figures

Every figure in the app can be opened in the figure studio, a window shared by the whole suite where you change the texts, the font size, the legend and the colors without touching the data, and export to PNG, SVG, PDF or TIFF at 300, 600 or 1200 ppi. Next to each figure, the ✎ button opens the figure editor, and two quick buttons download it as SVG or as a 170 mm PNG at 300 ppi. Downloads and the report always use the colors of the light theme, even if you are working in the dark one. Chapter 9 explains this in depth.

I.7The example data

So that you can learn without data of your own, the app comes with ten simulated tables: they were generated with models and parameters of the order of those published for each crop, with a fixed seed, so they are always the same. They are not measurements: they are there to learn the app and to see that each analysis responds as expected. Each tool offers them with Load example and marks them with the SIMULATED tag, and the Example data section of the home page gathers them, with a button to open each tool with its example loaded and another to download the CSV.

The tools that do not read a table—the calculators, temperature, the accelerated test, flow-through, modified atmosphere, precooling, the simulation of improvements, the ballots, randomization and all of Block 8—open with example values already typed in their fields, so that the result shows from the start.

I.8How a study is carried out

The blocks follow the product from harvest to the consumer. You do not need to go through all of them, nor in order: each tab works with its own data, and whatever you compute leaves its section in the report. The How it works section of the home page sums up the route in seven steps.

1. Measure (Block 2). Summarizes the quality of each lot over time, converts and compares colors, computes acidity, moisture and firmness, and turns damage scales and size grades into indices.
2. Model (Block 3). Fits the kinetics of an attribute, takes its constants to temperature and predicts shelf life; or, if what you have is the day each fruit was rejected, estimates the survival curves.
3. Breathe (Block 4). Measures respiration and ethylene, recognizes the climacteric and designs the package, precooling and refrigeration.
4. Quantify (Block 5). The losses of the chain in kilograms and in money, where improving pays off and from what height the fruit is bruised.
5. Evaluate (Block 6). With judges and consumers: whether the difference is noticed, how much it is liked, what penalizes it and how a panel describes it.
6. Compare (Block 7). The treatments of a trial throughout storage, with the analysis that matches how it was sampled. Block 8 adds the packaging, storage and transport calculations.
7. Publish (Block 9). The report with all of the above and the handling recommendations, and the project to continue another day.

I.9How it was checked

A computing program is worth what its numbers are worth. Every engine in PostHarvestPro was programmed from the published formula and compared, number by number, with an independent implementation: the R statistical environment (version 4.4.2) and its reference packages for nonlinear kinetics, survival analysis, sensory evaluation and trial analysis; published tables for color and psychrometrics; and hand computations written into the tests themselves for the calculators. Every comparison has its tolerance written down.

The comparison also served to correct. It caught, among others, a cutoff in the studentized range that set probabilities to zero with five or more means, standard errors of the logistic regression computed with the weights of the next-to-last iteration and an optimizer that declared convergence next to the pole of a second-order curve; all three were corrected before version 1.0. The details, with the tolerances of each test, are in the tests/validacion/ folder, which is the only part of the program that names software packages: the app and the rest of this manual describe the methods and cite the articles.

I.10What the program does not do

Knowing where a tool ends is as useful as knowing what it does. The app’s home page says so in What it does not do, and the chapters repeat it where it matters:

1.1The home page

When you open index.html, the app starts in Block 1. Unlike the other blocks, this one has no tabs and no data cards: it is a presentation page that you scroll from top to bottom, and the In this block list on the right leads to each of its sections.

At the top is the presentation panel. A small label states the subject of the app, Postharvest physiology and technology; below it comes the motto, Measure quality, predict shelf life and decide with data, and a paragraph that lists what it does, from quality indices and color to the packaging and storage calculators, and ends with two promises: every result states its method and its source, and the data never leave your computer.

1 2 3 4 5 6

• 1Start with an example → Opens Block 2›Quality summary and loads the example mango into it: the fastest way to see the app with data (Chapter 2).
• 2See the example data. Scrolls down to the Example data section of the same page (Section 1.4).
• 3Methods and sources. Scrolls down to the list of methods with their citation (Section 1.5).
• 4How to cite. Scrolls down to the program’s citation, at the end of the home page (Section 1.8).
• 5The four badges. Runs entirely in your browser, Validated against independent implementations, Spanish and English and SVG figures and 300 ppi PNG. They are only labels; they cannot be clicked.
• 6The illustration. A fruit in five stages of ripeness—Mature green, Breaker, Turning, Ripe and Overripe—over the firmness of three lots stored at 13, 20 and 25 °C, with the band of the market limit and the day the 20 and 25 °C curves cross it.

The illustration has its caption: Simulated: firmness falls with first-order kinetics; the warmer the store, the sooner shelf life ends. It is a drawing, not a result: it does not change with the data you load. But it sums up the central idea of the program, the one Chapter 3 turns into numbers: the same fruit, with the same initial firmness, reaches the limit on very different days depending on the temperature at which it is stored. The curves are drawn from left to right when the home page opens; if you turn animations off with the sparkles button in the top bar, or if your system asks for reduced motion, they appear already drawn.

The three buttons below only scroll the page. The first one, on the other hand, does the same as the Open in 2 · Quality summary button on the mango card in Example data: it changes block and tab, loads the table and shows the results.

1.2How it works: the route in seven steps

The first section below the presentation, How it works, sums up the route in seven numbered boxes (Figure I.5 of the introduction). Its subtitle explains it: The route follows the produce from harvest to the consumer. Each block takes your data (or an example), checks that they are complete, computes, explains the result in words and leaves its part in the report.

Block 8, Packaging and logistics, has no step of its own: its pallet, venting, storage and compatibility calculations go along with any of the steps, as Section I.8 says. The route is there so that you forget nothing, not to impose an order: each tab works with its own table, and you can go straight to Block 6 to analyze a tasting without having gone through the others.

1.3The nine blocks

The The nine blocks section has one card for each block from 2 to 9 (Block 1 is this very home page). Each one carries the block number, a drawing of its own made by code, a tag with the verb of what it does, the name of the block and the same line the app puts below its title. A click anywhere on the card opens the block. The subtitle of the section sums up the correspondence with this manual: A block is a module of the app and a chapter of the manual. Inside each one, tabs separate the tools.

At the foot of the home page, as at the foot of every block, a button leads to the next one: Next · 2 · Quality and maturity →. From the keyboard, Alt + → does the same.

1.4Example data

The Example data section gathers the ten simulated tables that come with the app, one per card (Figure I.4 of the introduction). Its subtitle gives the warning: Ten tables simulated with models and parameters of the order published for each crop. They are not measurements: they are there to learn the app and to check that each analysis responds as expected. Each button opens the tool with the example loaded.

Each card has the name of the data set with the SIMULATED tag, a description, the file in data/ it comes from with its number of rows, one Open in … button for each tool that uses it and the ⤓ CSV button, which downloads the table so that you can see its layout or use it as a template for yours. The table in Section I.7 says what each data set contains; the one below, where each button leads.

The mango also appears, without a button on the home page, in the Color, Ripeness and damage scales and Size grades tabs of Block 2, whose Load example button opens it right there. Each Open in … button does two things: it opens the tab and presses its Load example for you, which replaces whatever table that tool had.

1.5Methods and sources

The Methods and sources section lists the program’s 28 methods, each on a card with its name, the block where it is used and the works that define it, abbreviated by author and year. The subtitle sums up how they were programmed: Every method is programmed from its published formula and compared with an independent implementation; the tolerances and the results of that comparison are in the tests folder.

It is the same list, with the same abbreviations, as the Method and source: line of every result and the Methods and references section of the report, which includes only the methods of the blocks you used (Section 9.3). Appendix F gathers the 81 complete works, grouped by topic. If you are going to publish, cite the method you used as well as the program: the card says which one.

1.6Postharvest in brief

The Postharvest in brief section (The ideas behind the computations, in plain words.) has nine collapsible panels, each with the block where its idea applies. When the home page opens only the first one is expanded; a click on the title opens or closes any of them.

Each chapter of this manual comes back to these ideas in more detail in its “Theory in brief” boxes, next to the tool that uses them.

1.7What it does not do

Four boxes say plainly what cannot be expected of the program. They are the same limits that Section I.10 of the introduction tabulates, which adds two more (it does not simulate package dynamics or read instruments):

• It does not replace measurement. The models summarize data; extrapolating far from the temperatures, times or cultivars measured is the user’s responsibility, and the app warns when it happens. The most visible warning is in Block 3›Temperature, which flags as an extrapolation any storage temperature outside the measured ones.
• It brings no trade standards. The tables of sizes, permeabilities and compatibility are indicative and editable: use those of your standard, your film and your cultivar. The size-grade templates in Chapter 2 are an example of this.
• It does not model non-isothermal kinetics. Predictions are at constant temperature; variable temperature histories need k(T(t)) integrated over time.
• It uploads nothing. There is no server, account or connection: what you save is a project file on your computer.

1.8References and how to cite

The last two sections of the home page are the bibliography and the citation. In References, the See the 81 references panel opens the complete list of the works cited by the methods, in alphabetical order; it is the same list that Appendix F gathers, there grouped by topic.

How to cite begins with If PostHarvestPro helps your work, please cite it as: and gives the program’s citation in two forms, each with its button:

• The reference, in the language of the interface, copied with Copy the citation:
  Barrera-Guzmán, L. Á. (2026). PostHarvestPro: postharvest physiology and technology, quality, shelf life and sensory evaluation in the browser (Version 1.0.0) [Computer software]. Zenodo. https://doi.org/10.5281/zenodo.23935616
• The BibTeX entry, with the key barreraguzman2026postharvestpro, the English title, version 1.0.0, the year, the license GPL-3.0-or-later, the DOI and the address; it is copied with Copy BibTeX.

When you copy, a brief notice confirms Copied. The citation carries the Zenodo concept digital object identifier (DOI), which always resolves to the latest version. The same citation is at the end of Block 9 (Section 9.7) and at the end of every report. The home page closes with a footnote holding the User’s manual link, which opens this manual in another tab (with the interface in Spanish it reads Manual de usuario (en español) and opens the Spanish edition), and a line saying that PostHarvestPro 1.0.0 is free software (GPL-3.0) and part of the LABG Suite.

The block title sums it up in one line: Quality indices, CIELAB color, laboratory calculators, scales and size grades. Its five tabs are Quality summary, Color, Acidity, moisture and firmness, Ripeness and damage scales and Size grades. Three of them read a table and the other two are filled in by typing; all of them are recomputed as soon as you change a value. The thread of this chapter is the example mango: 72 simulated fruit, four per temperature and day, stored at 13, 20 and 25 °C.

2.1The data input of every tool

All the tools of the app that analyze a table—from the quality summary to the trials of Block 7—receive the data in the same box. It is explained here once; the other chapters only say which roles each tool asks for.

1 2 3 4 5 6 7 8 9

• 1The example strip. The name of the data set, the SIMULATED tag and its description. It is always there, even if you do not load it: it shows the layout of a table the tool understands.
• 2Load example. Loads the data set and runs the analysis. It is what the Open in … buttons of the home page press for you.
• 3⤓ Example CSV. Downloads the example table; it serves as a template for yours.
• 4Open file (CSV, TXT, XLSX, ODS). Reads a file from your computer: CSV, TSV or TXT separated by comma, semicolon or tab, or an XLSX, XLSM or ODS workbook. If the workbook has several sheets, a selector appears on the right to choose which one to read.
• 5Paste a table. Opens a box where you paste the cells copied from a spreadsheet, with the column names in the first row, and read them with Use the pasted table.
• 6…or drop the file here. Drag the file from your file explorer and drop it on the dashed box.
• 7The roles. One list for each piece of data the tool needs, with all the columns of the table. The app proposes the matching one by its name; you confirm it or change it. Roles marked (optional) can be left at — none —.
• 8A role with several columns. Some tools ask for several columns for the same role, with one check box per column; here, Attributes to summarize.
• 9See the data (72 × 13). Expands the table that was read, with its number of rows and columns, so that you can check it was read correctly (it shows the first 200 rows).

When a table is loaded, the analysis runs by itself, and runs again every time you change a column. If a required role is missing, the app does not compute and says so below the buttons: Choose the column for: …, with the name of the role. Other messages in the same place are The table has no rows with data. and Could not analyze: …, followed by the cause.

What the results have in common

Below the data, every tool shows its results with the same pieces, which the rest of the manual only names:

Every analysis you run also leaves its section in the report of Block 9 (Chapter 9), with its figures, its table and its reading.

2.2Quality summary

The first tab summarizes any set of quality attributes by group and by time: the mean with its dispersion, the course of one variable and the change between the first and the last sampling. It is the table that goes into any trial report, before modeling or comparing.

The Trial data card asks for one row per fruit or per sample. All its roles are optional: Group (temperature, treatment, lot), Time, Soluble solids (°Brix), Titratable acidity (%), L*, a*, b* and Attributes to summarize. With soluble solids and acidity, the app computes SSC/TA and BrimA for each fruit; with L*, a* and b*, chroma, hue, the citrus color index and the browning index (Section 2.3). Those computed variables are added to the attributes you tick.

With the mango, the app proposes temperatura as group, dia as time, sst, at, L, a and b in their roles and, as attributes, the numeric columns left free except those that identify the unit (fruto): peso_inicial_g, firmeza_N, ph, perdida_peso and antracnosis.

Above the results there are two controls. Show chooses what goes with the mean in the table: mean ± SD (the default), mean ± SE or mean and 95% CI, which writes the interval in square brackets. Variable of the figure chooses which variable is drawn; it opens with firmeza_N if there is one.

• Tiles. Observations 72; Groups 3 (temperatura); Times 8 (dia: the distinct values of the whole table); Variables 11, with the note includes the computed ones: the five ticked plus SSC/TA, BrimA, chroma, hue and the two color indices.
• Reading. The change of the figure variable between the first and the last time of each group, as a value and as a percentage: at 13 °C firmness went from 115.8 to 31.95 N between days 0 and 21 (−72.4%); at 20 °C, from 129.4 to 21.70 N between 0 and 12 (−83.2%); at 25 °C, from 121.5 to 4.75 N between 0 and 12 (−96.1%). It ends by pointing out the group that changed fastest, here 25, and refers to Block 7 to find out whether the differences are real and to Block 3 to model their rate.
• Figure. Course of firmeza_N: the mean of each group at each time with standard-error bars (Mean ± standard error.). If you choose no time, the figure is a bar chart, one bar per group.
• Table. One row per group and time—18 for the mango: eight times at 13 °C and five at 20 and at 25 °C—with its n and one column per variable. For instance, at 13 °C on day 0: firmness 115.8 ± 9.79 N, SSC/TA 7.39 ± 0.512 and hue 109.2 ± 1.42°; on day 21, SSC/TA 54.12 ± 8.59 and hue 79.77 ± 2.01°.

The Method and source: line reads Titratable acidity by titration (AOAC 942.15) · BrimA: Jordan et al. 2001 · Color: CIE 2018; McGuire 1992 · CCI: Jiménez-Cuesta et al. 1981 · BI: Palou et al. 1999: the last two are the sources of the color indices the summary computes.

2.3Color: converter and indices

The Color tab has three cards. The first, Color converter, translates a color between its three notations and computes the indices used in the postharvest literature.

Its hint says: Type the color in any of its forms: L*a*b* (D65 illuminant, 2° observer), RGB from 0 to 255 or its hexadecimal code. The others update and the swatch appears. The fields are L*, a*, b*, R, G, B, Hexadecimal and Pick, which opens the system color picker. It opens with L* 62, a* 8 and b* 48, the yellow of a ripe mango.

Below the fields, the swatch of the color with its code and its coordinates, and a note: inside the gamut of an sRGB screen or, if the color cannot be displayed, outside the sRGB gamut: shown is the nearest with the same L* and h°. The eight tiles with the starting values are:

The reading puts the hue into words: A hue of 80.5° reads as yellow in fruit that turn from green to yellow, orange or red; each crop has its own scale. The words come from fixed cuts of the angle: green from 105°, green-yellow from 85 to 105°, yellow from 70 to 85°, orange from 50 to 70°, red-orange from 25 to 50° and red below. They are a general guide, not the scale of your crop. The reading adds the chroma (Chroma (48.7) says how intense the color is, and L* how light.), and the method line gives the source of each tile: CIE 2018 (CIELAB, D65) · C*, h°: McGuire 1992 · CCI: Jiménez-Cuesta et al. 1981 · BI: Palou et al. 1999 · WI: Judd and Wyszecki 1975 · YI: Francis and Clydesdale 1975 · TCI: Hobson et al. 1983.

2.4Difference between two colors and the color of your data

Difference between two colors

The second card measures how distinguishable two colors are. Its hint says Color 1 is the reference (for instance, the initial one or that of a control). The fields are L* 1, a* 1, b* 1, L* 2, a* 2 and b* 2; they open with the green of a freshly harvested mango (64, −11, 36) and a ripe yellow (67, 9, 52). The Use the converter color as color 2 button copies the color from the previous card.

The tiles give the three difference formulas and their components: ΔE*ab (1976) 25.79, ΔE94 14.66 and ΔE00 (CIEDE2000) 15.45, the latter with its reading (perceived as different colors) and highlighted when it reaches 3.5; and ΔL* 3.00, ΔC* 15.13 and Δh° −26.8°, the difference in hue angle (color 2 is 26.8° less green). The reading puts it in one sentence—With ΔE00 = 15.45 the difference is so large that they are perceived as different colors—, gives the guide thresholds and recommends reporting ΔE00. In that sentence, the two highest grades read clear and so large that they are perceived as different colors; in the tile, as in the table below.

The color of your data

The third card reads a table with L*, a* and b* per fruit: L*, a* and b* columns, with group and time: the mean color of each group at each time, its ΔE00 from the group’s initial color and the course of hue. It asks for L*, a* and b* (required) and Group and Time (optional). Its Load example loads the mango.

The app averages L*, a* and b* of the fruit of each group and time, converts that mean into a screen color and computes its chroma, its hue and its ΔE00 with respect to the first time of the same group. The three figures are Mean color of each group at each time (Each cell is the mean of L*, a* and b* converted to sRGB.), Color change from the start (ΔE00) and Hue angle; below them comes the table with L*, a*, b*, C*, h°, ΔE00 and a Swatch of the color with its code.

The method line cites CIE 2018 (CIELAB, D65) · ΔE00: Sharma et al. 2005 · C*, h°: McGuire 1992.

2.5Acidity, moisture, firmness and weight loss

The Acidity, moisture and firmness tab brings together four laboratory calculators that read no tables: you type the readings and the result appears at once. They open with example values typed in.

Titratable acidity

For a titration with NaOH to pH 8.1 or to the phenolphthalein end point. The fields are NaOH used (mL) 8.2, NaOH normality 0.1, Sample (g or mL) 10, Made-up volume (mL) and Aliquot (mL)—empty: only if you diluted the sample and took part of it—, Dominant acid (citric, malic, tartaric, oxalic, lactic or acetic) and Soluble solids (°Brix) 14.5.

The milliequivalent is that of the chosen acid: 0.064 for citric (citrus, mango, papaya, tomato, strawberry, pineapple), 0.067 for malic (apple, pear, peach, plum, banana), 0.075 for tartaric (grape, tamarind), 0.045 for oxalic, 0.090 for lactic and 0.060 for acetic. With the starting values, acidity is 0.525% as citric, SSC/TA 27.6 (maturity index) and BrimA 13.45. Below, the same acidity Expressed as other acids: malic 0.549%, tartaric 0.615%, oxalic 0.369%, lactic 0.738% and acetic 0.492%.

Moisture and dry matter

With the three weighings of the dish (Weights of the empty dish, with the fresh sample and after drying to constant weight.): Empty dish (g) 32.415, Dish + fresh (g) 37.418 and Dish + dry (g) 33.212. They give Moisture (wet basis) 84.07%, Dry matter 15.93% and Moisture (dry basis) 527.7%, that is, grams of water per 100 g of dry matter.

Firmness

Converts a penetrometer reading: Reading 12.5, Unit (N, kgf, lbf or gf; it opens at kgf) and Plunger diameter (mm) 8. It gives the force in N (122.58), kgf (12.500) and lbf (27.558), and the Pressure on the plunger area, 2438.7 kPa. Pressure lets you compare readings taken with different plungers; force does not.

Weight loss

Initial weight (g) 312.4, Current weight (g) 298.7 and Days elapsed 9 give a Weight loss of 4.39%, computed on the initial weight, and 0.487% per day. When the loss reaches 5%, the tile turns amber and warns that it is near the limit at which many fruit shrivel.

2.6Ripeness and damage scales

Many attributes are rated by eye on a scale of classes: the ripeness stage from the skin color, the severity of a spot, the progress of a rot. The Ripeness and damage scales tab turns those ratings into a weighted index, the incidence and the percentage of marketable fruit of each lot.

The The scale card has an editable table with the Value and the Description of each class (Each class with its value (0 = sound, or the first grade) and its description. Edit it or pick a template.). It opens with the Damage 0–4 template—Sound, Slight (< 5% of the surface), Moderate (5–15%), Severe (15–30%) and Very severe (> 30%)—; the other two are Ripeness 1–5 (from Mature green to Overripe) and Decay 0–3 (from No decay to Rotten fruit). + Add row and × add or remove classes. Below, Market tolerance (highest class accepted) chooses the highest class that still sells; it opens at the second class, here class 1.

The The data card accepts two inputs. The first is a table with Class of each fruit (required) and Group and Time (optional); each combination of group and time is a lot. The second, in the …or type counts by lot panel, are counts typed by hand, one lot per line—for instance Lot A: 50, 20, 15, 10, 5—, which are read with Use the counts. If any rating matches no class of the scale, a warning says how many were left out of the count.

With the mango, the app takes antracnosis as the class, temperatura as group and dia as time: 18 lots of four fruit. The tiles read Lots or groups 18, Units rated 72, Highest index 50.0 (25 · dia 12, in amber) and Most marketable 100.0% (the first lot to reach it, 13 · dia 0, in green). The reading starts with the range of the index for the chosen scale—The weighted index (McKinney 1923) runs from 0 (everything in the lowest class, 0) to 100 (everything in the highest, 4).—and adds that, with the tolerance at class 1, marketable fruit runs from 50.0% to 100.0%. The figures are Distribution by class, one stacked bar per lot, and, when there are group and time, Weighted index over time, one line per group. The table gives for each lot its N, the percentage in each class, the Index, the Mean grade, the Incidence and the Marketable percentage.

The method line is Weighted index: McKinney 1923. The analysis is redone with the same data—the table or the typed counts—as soon as you choose another template, edit a class or change the tolerance.

2.7Size grades

The last tab sorts the fruit by size: how many fall in each grade, which one is the most frequent and how many are left outside the classes.

The The classes card has an editable table with Grade, Minimum and Maximum: Each grade with its minimum (included) and maximum (excluded, except in the last class), in the unit of your data. The templates are indicative: use those of your standard. There are three templates:

The The fruit card asks for Weight or diameter of each fruit and, optionally, a Group (lot, variety, origin). With the mango, the app takes peso_inicial_g.

The tiles read Fruit 72, Mean 298.9 g (SD 36.8), Most frequent grade Large and Outside the classes 0. The reading distributes the fruit: Large 59.7%, Medium 36.1%, Extra large 4.2% and Small 0.0%. With the Fruit per 4 kg box template, the most frequent grade is Count 14 (44.4%), followed by Count 12 (36.1%). If you choose a group, the figure shows one series of bars per group and the table one row per group. The method line recalls that the classes are editable and the templates a guide only (Kader 2002).

The block is called Kinetics and shelf life (in the bar, Shelf life) and introduces itself as “Reaction orders, temperature, accelerated tests and time to rejection.” It has four tabs: Kinetic models, Temperature, Accelerated test and Time to rejection. As everywhere in the program, there is no compute button: as soon as there are data, every change to a control redoes the calculations that depend on it.

The four tabs form a path. In Kinetic models you fit an attribute (firmness, color, vitamin C) against time at each temperature; the button Take the k values to the temperature analysis → passes the constants to Temperature, which fits them to Arrhenius and predicts the life at any temperature. Accelerated test does the same when what you have are not constants but shelf lives observed at high temperatures. Time to rejection is a different approach: it does not model an attribute, but the day on which each fruit stops being acceptable. The chapter uses two simulated examples: the example mango (the firmness of 72 fruit at 13, 20 and 25 °C) and the example chayote with two coatings (the days to rejection of 90 fruit).

3.1Kinetic models: the three orders

The Data card asks for an attribute measured over time and, if you wish, a group. Its text sums it up: “Each group is fitted separately with the three orders, by least squares on the original scale.”

The column roles are Time (in days, hours or weeks: the app does not convert units, and shelf life comes out in the unit you use), Attribute and Group (optional), which can be the temperature or the treatment. With the example mango (Load example in the strip, or Home›Example data) the app picks dia, firmeza_N and temperatura by itself. The table has thirteen columns (See the data (72 × 13)): you can swap the attribute for color (L, a, b), soluble solids (sst) or weight loss without loading anything again.

Below are four controls:

The three reaction orders

Almost all quality deterioration is described by one of three forms, which differ in how the rate depends on the value that remains. The app fits all three in each group:

A positive k means the attribute goes down; a negative one, that it goes up (the formation of a pigment, for example), and the reading warns about it with “Negative k: the attribute increases with time (formation).”

The table The three orders (Figure 3.2, bottom) shows for each group and each order its equation, k, the residual sum of squares (RSS), the AIC, the ΔAIC, the Akaike weight and, only as a classic reference, the Linearized R²; the row of the chosen order is shaded green. With the mango, first order wins at all three temperatures: at 13 °C with a weight of 0.971 (ΔAIC 7.02 over zero order), at 20 °C with 0.762 (second order is 2.33 behind and keeps a weight of 0.238) and at 25 °C with 1.000.

3.2Fit and life to the limit

The results card is called Fit and shelf life. Its tiles say how many groups were fitted, which order was chosen and how (by AIC or set by you), the Mean R² and, if there is a limit, the Life to the limit of each group.

With the example mango: 3 groups of temperatura, First order by AIC, mean R² 0.969 and life to the limit 25.9 · 10.4 · 6.3 days (limit 25). The reading in words gives, for each group, the order, k with its interval, the half-life and the day on which the attribute reaches the limit, also with its interval:

The intervals of k are written with three significant figures of their larger bound (which is why the one at 13 °C has four decimals and those at 20 and 25 °C, three), and the half-life and the time to the limit with one decimal, the same in the reading and in the table.

The reading closes with two checks: whether AIC chose the same order in every group (“AIC picks the same order in every group.”) and how many times the fastest constant is the slowest (here, 4.1). If the groups do not agree on the order, the reading recommends setting a single one: the k values of different orders do not have the same units and cannot be compared or taken to Arrhenius.

How the intervals are computed

The intervals of C₀ and k are Wald intervals with Student’s t and the degrees of freedom of the fit (n − 2), as the reading says: “The intervals are Wald intervals with Student’s t (95%).” The interval of the time to the limit is obtained by the delta method: the time is a function of C₀ and k (Table 3.2), and its variance combines those of the two parameters and their covariance.

The time at 13 °C (25.9 days) falls after the last day measured (21): it is a short extrapolation within the same model. If the attribute never reaches the limit with the chosen model—a zero order with negative k and a lower limit, for example—the reading says does not reach the limit and the tile shows a dash.

Below the reading appear, in smaller type and preceded by the group, the notes of the fit when there are any: for example, “Second order: could not be fitted and is left out of the comparison.” if one of the orders does not converge in that group. With the example mango the three orders are fitted at all three temperatures and no note appears.

Below the figure, the fit table (Figure 3.2, top) repeats these numbers with C₀ and k ± their standard error, the R² on the original scale and the number of fruit in each group (32 at 13 °C, because there it was measured up to day 21; 20 at 20 and 25 °C). Both tables are downloaded with ⤓ CSV and ⤓ XLSX, and the figure with the buttons of its frame (Chapter 2, Section 2.1). The methods are those of Labuza (1984) and van Boekel (2008), with the nonlinear least squares of Bates and Watts (1988) and the AIC of Burnham and Anderson (2002).

3.3Temperature: Arrhenius, Q10 and square root

The Temperature tab fits the dependence of k on temperature with three models and, with it, predicts shelf life at any temperature. Its input card, “Rate constants at several temperatures,” is an editable table: “Type k (with its standard error, if you have it, to weight) or bring them from the kinetic models.”

The table has the columns Temperature (°C), k and SE of k (optional); + Add row adds one and the × of each row removes it. At least two different temperatures with positive k are needed (three for the square root). Below, the checkbox Weight by the standard error of k (unchecked) and the Reference temperature (°C) (20), at which k is reported.

The tab already opens with the constants of the example mango, fitted as Kinetic models fits them with its default values (order by AIC, nonlinear, 95%): 0.06119 ± 0.0027 at 13 °C, 0.1569 ± 0.0093 at 20 °C and 0.2508 ± 0.0089 at 25 °C, with first order and C₀ = 123.736 (the mean of the three C₀) in the shelf-life section. So opening it directly or reaching it with the button gives the same Eₐ.

The button Take the k values to the temperature analysis →, at the foot of Fit and shelf life, does the same with your data: it first sets the chosen order, the mean of the C₀ and the limit in the shelf-life section, then copies the k and the standard error of each group to the table and opens the tab, so that everything, shelf life included, is computed with the new values. It only works if the group is the temperature written as a number; otherwise it warns “For Arrhenius the group must be the temperature (numbers).” The table shows k with four significant figures and its standard error with two, like the fit table, but it stores and uses the full value until you type another one in the cell.

The three models

With the mango k values, the card Arrhenius, Q10 and square root gives:

The reading puts it into words: “With Eₐ = 84.2 kJ/mol, every 10 °C more multiplies the deterioration rate by 3.54 near 5 °C and by 3.01 near 25 °C: Q10 is not constant.” Between the measured temperatures, Q10 is 3.84 from 13 to 20 °C and 2.56 from 20 to 25 °C. Below, the table compares each measured k with the one Arrhenius predicts (0.06119 versus 0.06293 at 13 °C, for example) and gives Q10 at each temperature (3.30, 3.12 and 3.01).

3.4Shelf life at any temperature

The lower part of the same card, Shelf life at any temperature, combines the Arrhenius line with the order, the initial value and the limit to predict how many days the product lasts at the temperature you choose.

The controls are Order (Zero, One or Two; by default, One), Initial value C₀ (123.736, that of the mango), Limit (25), Storage temperature (°C) (10) and Interval: Of the mean (the expected life of a typical lot) or Prediction (that of a new lot, which adds the scatter of the points around the line and is wider). If the limit is larger than C₀, the app understands that the attribute rises.

The interval of the life is obtained by passing that of k(T) through the formula for θ; the uncertainty of C₀ is not propagated. The tiles give the Shelf life at that temperature with its interval and the corresponding k; if the temperature is outside the measured ones, a third, amber tile appears: Caution · extrapolation · outside 13–25 °C.

At 13 and 20 °C the prediction does not exactly repeat the life of the direct fit (25.4 versus 25.9, 10.9 versus 10.4), because it uses the k smoothed by Arrhenius and a single C₀, the mean of the three. That is the right way to read it: the line summarizes the three temperatures at once.

3.5Accelerated test

An accelerated test stores the product at temperatures higher than its storage temperature so that it deteriorates in days instead of weeks, and extrapolates the life to the real temperature. The Accelerated test tab makes that extrapolation from the observed lives, without going through the constants.

The card Shelf lives at high temperatures is an editable table with Temperature (°C) and Observed shelf life (in days, weeks or whatever unit you use: The example is illustrative.). It comes with six tests, two at each temperature: 4.8 and 5.3 days at 30 °C, 3.1 and 2.8 at 35 °C, 2.1 and 1.9 at 40 °C. At least three lives at two different temperatures are needed. The controls are Model—Arrhenius (ln θ against 1/T) or Q10 (ln θ against T)—and Storage temperature (°C) (20).

The Prediction card gives the life at the storage temperature (the geometric mean the line predicts) with its prediction interval, which is the one that corresponds to a new test at that temperature and is almost always wide. With the model Q10 (ln θ against T) the life at 20 °C becomes 12.4 days [8.5, 18.3], with Q10 2.53 (constant in the model), Eₐ 68.4 kJ/mol and R² 0.9744: the two models are similar between 30 and 40 °C and diverge when extrapolating. The reading warns in bold “Extrapolation outside the tested temperatures.” when the storage temperature lies outside those of the test, which in an accelerated test is always.

3.6Time to rejection: Kaplan–Meier

In some trials what is measured is not a continuous attribute but the day on which each fruit stops being acceptable: a rot appears, it shrivels, the panel rejects it. The Time to rejection tab analyzes them as survival data: “One row per fruit: the time until it was rejected (or until the last day it was seen sound) and whether it was rejected (1) or still acceptable at the end (0, censored).”

The roles are Time to rejection or censoring, Rejected (1) or censored (0) and Treatment (optional). The example is the chayote with two coatings: 30 fruit per treatment (control, vegetable wax and chitosan, which the data name Testigo, Cera vegetal and Quitosano) at 10 °C, in a trial that ended at 35 days; the app picks dias, rechazado and tratamiento by itself. The controls are Kaplan–Meier interval (Log, Log-log or Plain), Parametric model (The one with the lowest AIC, Weibull, Log-normal, Log-logistic or Exponential) and Tolerated rejection (%) (10, from 1 to 99).

The card Survival curves opens with five tiles: Fruit 90, Rejected 75 (83.3%), Censored 15 (still acceptable at the end), Log-rank χ² = 22.48, p < 0.001 (df 2), and Best model Weibull by AIC. The log-rank test (Mantel 1966) compares the complete curves of the treatments; if they differ, the reading names the one that keeps the fruit acceptable longest: Quitosano.

Below, the table by treatment (Figure 3.8, top) gives the Median (KM)—the day on which the curve crosses 50%—with its interval, the Restricted mean (the area under the curve up to the last day observed, ± its error), the Time to 10% and the Median (model), these two from the parametric model:

The interval of the chitosan median has no upper bound (∞): its upper confidence curve never falls below 50% before the trial ends. This is not an error, but the way of saying that the trial did not last long enough to bound that median. The restricted mean is useful precisely in those cases, because it always exists; but it depends on the day the trial was cut off and is compared only between treatments observed for the same time.

3.7Parametric models and time ratios

Kaplan–Meier describes without assuming a shape; a parametric model assumes a distribution of the time to rejection and, in exchange, gives the time of any percentage of rejection, even outside the observed days, and a single measure of the effect of each treatment.

The app fits four failure-time models with censoring (Lawless 2003), all with one parameter per treatment: Weibull (the hazard of rejection rises or falls with time), log-normal and log-logistic (the hazard rises and then falls) and exponential (constant hazard, the special case of Weibull with shape 1). The table Parametric models compares them by their log-likelihood and their AIC:

With the chosen model, the reading gives the day on which the tolerated percentage is rejected: “With the Weibull model, 10% of the fruit are rejected around day Testigo 8.4 [6.6, 10.7], Cera vegetal 11.7 [9.3, 14.7], Quitosano 14.0 [11.2, 17.6].” With Tolerated rejection (%) at 50, these are the medians of the model: 17.5, 24.4 and 29.3 days, very close to those of Kaplan–Meier (18.0, 26.5 and 29.5). If you set another model, the reading names it (“With the log-logistic model, …”) and the numbers change little with the log-normal (8.3, 11.6 and 14.9 days) or the log-logistic (8.7, 12.4 and 15.1), and a lot with the exponential (1.9, 3.0 and 4.3): a constant hazard predicts rejections from the first day, which did not happen in the chayote (the first was around day 6).

As in Kinetic models, the reading ends with the notes of the calculations, if any, preceded by the treatment or the model they refer to: those of Kaplan–Meier in each treatment, those of the chosen model and, for each model in the comparison whose maximum likelihood did not converge, “maximum likelihood did not converge; its AIC is approximate.” With the example chayote the four models converge and there are no notes. If no fruit was rejected (all censored), there is nothing to fit: the card keeps only the tiles Fruit, Rejected and Censored and the reading says “No parametric model could be fitted: rejected fruit (status 1) are needed.”

Time ratios

The four models are accelerated failure-time models: the treatment stretches or shrinks the time scale. Its effect is summarized in a time ratio against the first treatment (the reference); the app explains it this way: “A time ratio of 1.4 means that the treatment lengthens the time to rejection by 40% compared with the reference group.” With Weibull, vegetable wax lengthens the time to rejection 1.391 times [1.129, 1.714] and chitosan 1.671 times [1.333, 2.094]: 39% and 67% more than the control, and neither interval includes 1. The methods cited are Kaplan and Meier (1958), Greenwood (1926), Mantel (1966), Lawless (2003) and Hough et al. (2003), who apply these ideas to sensory shelf life.

Block 4 is subtitled “Respiration rates, climacteric, modified-atmosphere packaging and precooling.” It has five tabs: Static system, Flow-through, Climacteric, Modified atmosphere and Precooling and heat load. Only two read a table through the common data entry (Section 2.1): the static system and the climacteric, with the simulated example “Hass” avocado in three jars and over twelve days (Section I.7). The other three open with values already written in their fields and tables, and recompute as soon as you change one.

4.1Static system

The simplest way to measure respiration: the produce is sealed in a jar of known volume and you read how CO₂ rises—and, if you have the means, how O₂ falls and ethylene builds up—at several times. The rate comes from the slope of each gas against time.

The Readings in a closed jar card asks for two required columns, Time (h) and CO₂ (%), and five optional ones: O₂ (%), Ethylene (µL/L), Jar or replicate, Mass (kg) and Jar volume (L). With the jar column, the app computes each jar separately and then averages. Below there are five fields:

• Mass (kg), if there is no column (0.65) and Jar volume (L), if there is no column (3.8): used only when the table does not have those columns.
• Produce density (kg/L) (1.0): to subtract from the jar the volume the produce takes up.
• Temperature (°C) (20) and Pressure (kPa) (101.325): for the molar volume of the gas, which converts milliliters into milligrams.

The results card, Respiration rate and ethylene production, gives six tiles: CO₂ in mg kg⁻¹ h⁻¹—the mean of the jars, with its standard error and the number of jars—and in mL kg⁻¹ h⁻¹, O₂ in mL kg⁻¹ h⁻¹, the Respiratory quotient, ethylene with its class, and the Heat of respiration in W per metric ton and in kJ per metric ton and day. Then come the reading, two plots—CO₂ build-up and O₂ depletion (or Ethylene build-up if there is no O₂), with the points and the line of each jar and a legend with their names—and the table by jar with the mass, the free volume, the CO₂ rate and its R², the O₂ rate, the RQ and ethylene.

Kader’s classes

The app classifies ethylene with Kader’s (2002) classes, defined at 20 °C: very low below 0.1, low from 0.1 to 1, moderate from 1 to 10, high from 10 to 100 and very high above 100 µL kg⁻¹ h⁻¹. The same author’s respiration classes are defined at 5 °C; that is why the app does not assign a class to a respiration measured at another temperature, and the reading reminds you: “Kader’s (2002) classification is defined at 5 °C: compare it with a measurement at that temperature.” The example avocado, measured at 20 °C, can only be compared with other fruit at 20 °C.

4.2Flow-through

In the flow-through system a stream of air passes through the produce chamber without stopping; once it is steady, the difference in concentration between inlet and outlet, times the flow, is what the produce respires. It is the method for measuring over days without the atmosphere changing.

The Chambers with air flow card is an editable table, one row per chamber, with Chamber, Mass (kg), Flow (mL/min), CO₂ in (%), CO₂ out (%), O₂ in (%), O₂ out (%), Ethylene in (µL/L) and Ethylene out (µL/L); on a narrow screen the table scrolls sideways. A new row (+ Add row) comes with the inlet air already written (0.04% CO₂, 20.95% O₂ and 0 ethylene). Below, the Temperature (°C) (20) is used to convert milliliters into milligrams. A row without mass or without flow is not computed.

with F in mL/min. For O₂ the difference is inlet minus outlet. The Rates by chamber card gives four tiles with the mean of the chambers—CO₂, O₂, RQ and ethylene—and the table by chamber, which adds CO₂ in mL and the heat in W/t and gives ethylene in the Ethylene µL kg⁻¹ h⁻¹ column (Fonseca et al. 2002; Saltveit 2016).

With the starting values, chamber A (2.1 kg; CO₂ from 0.04 to 0.42%) respires 29.80 mg CO₂ kg⁻¹ h⁻¹, B 28.82 and C 30.69; the three release 85 to 91 W per metric ton. Chamber A produces 1.3286 µL of ethylene kg⁻¹ h⁻¹, B 1.2600 and C 1.4318.

4.3Climacteric

Climacteric fruit—avocado, mango, banana, tomato—show, as they ripen, a rise in respiration together with a burst of autocatalytic ethylene; non-climacteric fruit—citrus, grape, strawberry—do not. Knowing which type a fruit is decides whether it can be harvested green and ripened at destination.

The Respiration and ethylene curves card asks for Time and Respiration (CO₂ per kg and hour) and, optionally, Ethylene (µL kg⁻¹ h⁻¹), measured on the same fruit along ripening. Below there are five fields. The first two say what units the data are in, to write them in the tiles, the reading and the plot axes:

• Time unit: days or hours;
• Respiration unit: mg CO₂ kg⁻¹ h⁻¹ or mL CO₂ kg⁻¹ h⁻¹.

The app proposes them from the name of the column you choose: dia, dias or day gives days, and hora, hour or a name ending in _h gives hours; a respiration name with “ml” gives mL and one with “mg,” mg. If the proposal is wrong, change it: the units do not change any calculation, only how the results are written. Ethylene is always expected in µL kg⁻¹ h⁻¹. The other three fields set the rule:

• Minimum respiratory rise (×), 1.5 by default;
• Minimum ethylene rise (×), 10;
• Minimum ethylene peak (µL kg⁻¹ h⁻¹), 1.

The Ripening pattern card gives the Pattern, the Respiratory rise with its minimum and its peak in the respiration unit, the Respiration peak with its time and value, and the Ethylene peak with its time, value and rise. The reading writes out the rule with the thresholds you set and interprets it. The two plots, Respiration and Ethylene production, label the axes with their units—Time (days), Respiration (mg CO₂ kg⁻¹ h⁻¹) and Ethylene (µL kg⁻¹ h⁻¹) in the example—and mark with vertical lines the minimum and the peak the rule used.

For the example avocado, with the columns dia and respiracion_mg, the app proposes days and mg CO₂ kg⁻¹ h⁻¹. The tiles say “Respiration peak: day 6 · 133.0 mg CO₂ kg⁻¹ h⁻¹” and “Ethylene peak: day 7 · 83.22 µL kg⁻¹ h⁻¹ · × 554.8.” The pattern is climacteric, and the reading adds that “ethylene peaks 1 day after respiration.” After the peaks, respiration falls to 42.7 on day 10 and rises a little again at the end (54.5 on day 12), like fruit entering senescence. When ethylene peaks before respiration, the reading attributes it to autocatalytic production; when they coincide (less than half a unit apart), it says the peaks go together.

4.4Modified atmosphere: produce and package

Inside a sealed bag, the produce consumes O₂ and produces CO₂ while the film lets O₂ in and CO₂ out. Over time the two flows balance and the bag reaches an equilibrium atmosphere. If that atmosphere falls within the window the produce tolerates, respiration slows down and shelf life is extended; if O₂ falls too low, the produce ferments.

The tab does not read a table: the Produce and package card opens with a written case—a bag of avocados—and recomputes with every change. Its fields, in three rows:

The produce list has ten windows: avocado, mango, papaya, banana, mature-green tomato, strawberry, blueberry, sweet cherry, broccoli and apple. Choosing one changes only the four window fields; respiration, mass and package stay as you wrote them, so change them too.

The films

The Film permeabilities (editable) drop-down holds a table of nine films: low-density polyethylene, linear low-density polyethylene, high-density polyethylene, cast polypropylene, biaxially oriented polypropylene, plasticized poly(vinyl chloride), ethylene–vinyl acetate, oriented polystyrene and polyester (PET). For each one it gives P O₂ and P CO₂ in mL·µm m⁻² d⁻¹ atm⁻¹ at 23 °C and the activation energies Eₐ O₂ and Eₐ CO₂ in kJ/mol, with which the app corrects the permeability to the package temperature:

At 8 °C, low-density polyethylene lets through less than half the O₂ it does at 23 °C: cold closes the film almost as much as it slows respiration. These are indicative values (Mangaraj et al. 2009): the card warns you and asks for those on your film’s data sheet. You can correct a row or add a film with + Add row; the new one appears in the Film selector.

4.5The equilibrium atmosphere and the film thickness

At steady state, what the produce respires equals what crosses the film. From that balance come the O₂ and CO₂ of the bag, the thickness that would bring O₂ to the center of the window, and the permeability ratio needed for CO₂ to fall inside it as well.

with W the mass in kg, L the thickness in µm, A the area in m², and the factor 24 because respiration is per hour and permeability per day (Exama et al. 1993; Fishman et al. 1996). A key property follows: all the atmospheres a film can give, whatever the thickness, area or mass, lie on a straight line that starts at air with slope RQ/β, where β = P_CO₂/P_O₂ is the permeability ratio of the film. The thickness only moves the point along its line; to change lines you have to change films.

The Equilibrium atmosphere card gives five tiles: O₂ inside and CO₂ inside with their window (green inside it, amber outside and red if there is anaerobiosis), the Bag area, the β of the film with the β needed, and the Thickness for the target O₂—the center of the O₂ window—with the chosen film. The reading says whether the atmosphere falls inside or outside, lists the films that, at the thickness that brings them to the target O₂, also keep CO₂ inside the window, and recalls the assumptions. The Possible atmospheres of each film plot is the O₂–CO₂ plane with the line of each film—named, with its β, in a column legend on the right—, the window and the package point, labeled “this package” over a light halo so it reads on top of the lines; the table gives for each film its β, the thickness for the target O₂, the resulting CO₂ and whether it stays inside the window.

A thickness outside 8–150 µm cannot be made or sealed as a bag: the table marks it “(not practical)” and the film does not count as a solution even if its CO₂ falls in the window, like PET, which would need 0.4 µm. When no film gets there, the reading says so and gives the β that would be needed, “or microperforations”: that is what happens with mango (window 3–5% O₂ and 5–8% CO₂, β needed ≈ 2.36), which with the same bag finds no film in the table.

4.6Precooling

Removing field heat as soon as possible is the cheapest way to extend shelf life. Precooling—with forced air, water, ice or vacuum—lowers the pulp temperature following, after an initial lag, an exponential curve toward that of the medium.

The Cooling curve card is an editable table of Time (h) and Pulp (°C), with the Medium temperature (°C) (1) and the Target temperature (°C) (5). It opens with a simulated forced-air curve: ten readings from 0 to 5 h that fall from 28.0 to 2.7 °C. At least three readings are needed. The app fits the exponential law to the dimensionless temperature:

by least squares on ln Y, with T_i the first reading. C is the cooling coefficient (h⁻¹) and j the lag factor: how long heat takes to start leaving the center of the fruit or the package; j = 1 means no lag (Thompson et al. 2008).

The Cooling times card gives the Half cooling, the Seven-eighths (“commercial reference”), the time To the target temperature, and j · C with the R² of the fit. In the starting curve, j = 1.063 and C = 0.566 h⁻¹ (R² 0.9991). The fitted curve starts slightly above the first reading (28.0 °C) precisely because j > 1.

4.7Refrigeration load

The refrigeration equipment must remove, in the time available, the field heat of the produce, that of the packaging, the heat the produce generates by respiring and whatever comes in from elsewhere. The Refrigeration load card, on the same tab, adds it up and turns it into capacity.

Its fields, with the starting values: Produce (kg) 10,000, Water content (%) 85, Initial temperature (°C) 28, Final temperature (°C) 8, Time available (h) 6, Respiration (mg CO₂ kg⁻¹ h⁻¹) 60, Packaging (kg) 800, Packaging specific heat (kJ kg⁻¹ K⁻¹) 1.4 and Other loads (%) 20 (infiltration, fans, lights and people). The respiration must be that of the produce at the mean temperature of the cooling.

The specific heat comes from the water content by Siebel’s (1892) formula, and the capacity is also given in tons of refrigeration (1 TR = 3.517 kW).

Reading the block’s results

Block 5 is subtitled “Quantity and value lost by stage, critical points, what-if and mechanical damage.” It has three tabs: Losses by stage, Simulate improvements and Mechanical damage. The first two work on the same chain, which you write in an editable table; the third reads a table through the common data entry (Section 2.1). Both examples are the example saladette tomato, simulated: a six-stage chain and a drop test with 60 fruit (Section I.7).

5.1The chain: stages, loss and price

A postharvest chain is a succession of stages—harvest, sorting, collection, transport, wholesale, retail—and what is lost at one never reaches the next. That is why the loss of each stage is expressed over what enters it, and losses accumulate.

The The chain card is an editable table, one row per stage and in order, with four columns:

• Stage: the name, as you want it to appear in the plots.
• Loss (% of input): the percentage of what reaches that stage that is lost there.
• or loss (kg): the loss in kilograms, if you measured it that way; when a row has kilograms, the app uses them and sets the percentage aside (and does not let a stage lose more than entered it).
• Price per kg: what a kilogram is worth at that stage.

Below come the Quantity entering the chain (kg) (10,000) and the Currency ($), which only changes the symbol in the results. The tab opens with a short four-stage chain written at the start (Harvest, Packing, Transport and Retail), in which 7803 of the 10,000 kg reach the end. The Load example button in the example strip—this card has its own, not the common data entry—replaces it with the tomato chain, and so does Open in … on the home page. The example chain keeps its stage names in Spanish, as the app shows them: Cosecha (harvest), Selección y empaque (sorting and packing), Acopio (collection), Transporte (transport), Central de abasto (wholesale market) and Venta al menudeo (retail). A row without a name, or without a percentage or kilograms, does not enter the calculation.

5.2Losses in quantity and value

The Losses in quantity and value card sums up the chain in five tiles, a reading, a Sankey diagram, two bar charts and the table by stage.

The tiles are Enters the chain, Reaches the end (with its percentage), Is lost (with the loss index), Value lost (“at the price of each stage”) and Value at the final price (“what the market would have paid”). The reading says how many kilograms of every 100 reach the end, which stage loses most kilograms and which most money, and names the critical points (Section 5.3).

In the Sankey diagram the width of each band is proportional to the kilograms: the green band narrows stage by stage and from its lower edge falls, in red, what is lost, with its kilograms and percentage. Each column carries the stage name and the kilograms that leave it. The two bar charts, Loss by stage (kg) and Value lost by stage, set the stages side by side to compare them.

Below the Pareto table (Section 5.3), the Send to EconomicsPro → button downloads the chain as chain_losses.csv—stage, in_kg, lost_kg, loss_pct, price_kg, value_lost and out_kg—and opens EconomicsPro, the suite’s application for the economic evaluation of projects, in a new tab; a notice reminds you to open the file in its data block. Opening that application online is the only thing in this block that needs a connection; the CSV is downloaded anyway.

5.3Critical points

Not all stages weigh the same. Pareto analysis sorts the stages from largest to smallest loss and flags those that, together, add up to 80%: the critical points, where it pays to look first.

The Critical points (Pareto) table sorts the stages by Kilograms lost, with their Share of the loss and the Cumulative share, and next to it the order by value (Stage by value, with its share of the value lost). The shaded rows are the critical points in kilograms. The app takes the stages, in order, until the cumulative share reaches 80%, including the one that crosses it.

In the example, the critical points in kilograms are Selección y empaque, Venta al menudeo, Central de abasto, Cosecha and Transporte; in value, Venta al menudeo, Central de abasto, Selección y empaque and Transporte. That the kilogram criterion points to the start of the chain and the money criterion to the end is usual: what is lost early weighs more, what is lost late is worth more. In a chain with losses as even as this one, 80% covers almost every stage; Pareto discriminates better when one or two stages concentrate the loss.

5.4Simulate improvements

What would happen if a stage lost half of what it loses today? The Simulate improvements tab computes it on the chain of Losses by stage and compares the same improvement at every stage.

The What if the loss of one stage falls? card has two controls: Stage, with the stages of the chain, and Reduction of its loss (%) (50), relative: 50% means losing half of what is lost today at that stage. If the chain does not exist yet, it warns: “First build the chain in ‘Losses by stage’.” The results, in Result of the simulation, are three tiles—Extra arriving, Value gained at the final price and New loss index with the previous one—, the reading, the chart Value gained by reducing the loss of each stage by 50% (the chosen stage in orange) and the table with the extra kilograms arriving, the value gained and the new index for each stage.

The proposed Stage is the one that loses most value in the chain. When the chain changes its stages—when you load the tomato example, for instance—, the selector again proposes the one that loses most value in the new chain; if you only correct a figure of the same chain, it keeps the stage you chose.

5.5Mechanical damage: curves and threshold

The impacts of harvest, the packing line and transport leave bruises that are not visible at first but rot or are rejected later. A drop test from several heights tells how much damage each height produces and from which one it begins.

The Impact or compression test card asks, one row per fruit, for Height, energy or force—required—and five optional columns: Bruise size (curves) (area, volume or depth of the bruise), Bruised (0/1), Bruise volume (mm³), for the susceptibility, Impact energy (J) and Fruit mass (g), if there is no energy. The card’s hint sums it up: “optionally whether it was bruised (0/1), the bruise volume and the impact energy (or the mass, to compute it as m·g·h), which give the susceptibility.” With the example, the app picks altura_cm, area_mm2 for the curves, danado, volumen_mm3, energia_J and masa_g.

With the bruise size, the app fits four curves by least squares and compares them by their AIC: linear (y = a + b·x), quadratic (y = a + b·x + c·x²), power (y = a·xᵇ) and exponential (y = a·e^(b·x)); the last two are fitted on the log scale, as is customary in the impact literature, and only with fruit of positive size and height (Mohsenin 1986). The table gives the coefficients in the Coefficients (a · b · c) column—those of the equation as written, with a on the original scale also in the power and exponential curves—, the R², the AIC and the number of fruit for each curve, and shades the one with the lowest AIC. The Damage against plot for the chosen variable draws the fruit, the line and, if it is another one, the curve with the lowest AIC. Titles and axes read the column name as a label with its unit: altura_cm is written “Height (cm)” and area_mm2, “Bruise area (mm²).”

Although the power and exponential curves are fitted on the log scale, the table gives a = e^{ln a}, the coefficient of the curve as written: the power curve of the example is y = 1.169·x^1.298, and the exponential one, y = 20.95·e^0.04364·x.

The threshold and the susceptibility

The Damage threshold is the height where the line crosses zero, −a/b, in the unit of the column (here, cm): below it, according to the line, no visible damage is expected.

The Bruise susceptibility is the measure of Bajema and Hyde (1998): the bruise volume per joule of energy, in mm³/J. The app computes it fruit by fruit, volume over energy, and averages over the fruit with a measured bruise (volume greater than zero). It takes the volume from Bruise volume (mm³), for the susceptibility; if you do not choose it, it uses the size of the curves. It takes the energy from Impact energy (J); if there is none, from the x axis when that is an energy; and otherwise it computes it from the mass and the height, E = m·g·h. The tile says where it came from: “volume of the bruise per joule” and the number of fruit. The reading explains it in a paragraph of its own.

5.6Incidence and logistic regression

The size of the bruise is not everything: for a packer, what matters is what proportion of fruit comes out bruised. With the Bruised (0/1) column, the app fits a logistic regression of incidence against height and computes the heights that bruise 50% and 10% of the fruit.

The coefficients are estimated by iteratively reweighted least squares, and the 95% confidence interval of each height, which is a ratio of two coefficients, by Fieller’s method (Finney 1971). The column must contain only zeros and ones; if it contains anything else, the app does not fit the logistic. The Bruises 50% and Bruises 10% tiles give the two heights with their interval, and the Bruise incidence plot draws the observed proportion at each height, the logistic curve and two dashed lines at 0.5 and 0.1.

Under its title, the app sums up the block: “Discrimination, affective and descriptive tests, with the design of the tastings.” One line below, it refers you to SensorialPro, of the same suite, for advanced tests, panels and preference maps, and notes that that app opens the CSV files exported here without changes. The tools are in six tabs: Discrimination, Hedonic, Just-about-right, CATA, Descriptive profile and Ballots.

The examples are three simulated coffee tables: cafe_discriminativas.csv (three tests between the “Altura lavado” (washed high-grown) coffee and the “Honey” one), cafe_consumidores.csv (80 consumers who rate four coffees—Altura lavado, Natural, Honey and Comercial (commercial)—on the hedonic scale, three just-about-right scales and ten CATA terms; the same table feeds the Hedonic, Just-about-right and CATA tabs) and cafe_descriptivo.csv (a panel of eight judges). The data are in Spanish, so the products, attributes and terms keep their Spanish names in the app and in this chapter. The data entry and what the results have in common—tiles, reading, figures with SVG, PNG and ✎, tables with ⤓ CSV and ⤓ XLSX, and the Method and source: line—are explained in Section 2.1.

6.1Discrimination tests and d′

A discrimination test asks whether the judges can tell two samples apart: the coffee with and without a treatment, the fruit from two atmospheres. The app does not stop at the p-value: it turns the correct answers into the Thurstonian d′, which tells how large the difference is on a scale common to every method.

The table of tests

The Test results card does not read a file: it is an editable table, one row per test, which already opens with a starting row (“Test 1”, triangle, 21 of 42). Load example replaces it with the three coffee tests; + Add row adds another and × removes it. Every change recomputes.

Below, Confidence (90, 95 or 99%; 95% by default) sets the level of the intervals and also the α of the test (α = 1 − confidence). Statistic chooses the test: Exact binomial (the default, with the Clopper–Pearson interval), Likelihood ratio (with the profile likelihood interval), Score (Wilson’s, with continuity correction) or Wald. With few judges, stay with the exact one.

Difference and its size (d′)

For each difference test, the results card writes the correct answers, whether the samples can be told apart (p < α) or no difference is shown, the p-value with the correct answers that were needed (the minimum with which the test is significant for that total), d′ with its interval, and pd. A note recalls the scale: “a d′ near 1 is a small difference few notice; above 2, a clear one.” The table, downloaded as discrimination_tests.csv, gives pc and pd with their intervals, d′ with its standard error (by the delta method) and the interval of d′, which is that of pc carried through the same function.

The similarity test

If what you want to show is that a process change is not noticed, change the Kind to Similarity and set pd₀. The hypothesis is reversed: the test is significant when the correct answers are few, and the reading says “similarity is shown: the proportion of discriminators is below 0.20” or “similarity cannot be claimed with pd₀ = 0.20”. Not showing a difference is not showing similarity: with the 21 correct of 42 of the triangle, the similarity test with pd₀ = 0.2 gives p = 0.722; with 16 correct of 60, p = 0.001.

The Method and source: line cites the Thurstonian models (Ennis 1993; Brockhoff and Christensen 2010), Bi (2006) and the Clopper–Pearson interval.

6.2Planning: judges and power

The question worth asking before the tasting, not after: for the difference I care to detect, how many judges do I need and which method performs best? The Plan: number of judges and power card needs no data.

The fields are Method (Triangle), d′ you want to detect (1.5), α (0.05), Desired power (0.8) and Judges available (30). The four tiles give the Judges needed (53, “for power 0.80”), the Power with 30 (0.600, marked “low” for being below 0.8), the Critical correct with 30 (15: the number of the 30 judges who would have to answer correctly for the test to be significant) and pc / pd (0.506 / 0.260: the proportion correct and of discriminators that corresponds to d′ = 1.5 in that method).

The table compares the five methods with the same d′, the same α and the same power:

The reading sums it up: “the triangle test needs 53 judges. The most efficient method for this difference is the 3-AFC test (9 judges).” The two figures show why. Psychometric functions plots pc against d′ for the five methods, with a line at the chosen d′: the 2-AFC and the 3-AFC rise much faster than the triangle and the duo-trio. Power against number of judges plots the exact power from 6 to 123 judges, with a line at the desired power.

6.3A–not A and paired preference

Two small cards at the bottom of the tab, with typed fields and an immediate result: the A–not A test, for when the samples cannot be served together, and paired preference.

A–not A

The judges first learn what sample “A” is like and then, for each sample, say whether it is “A” or “not A”. The fields are “A” to A samples (33), A samples (40), “A” to not-A samples (18) and Not-A samples (40). The hits are H = 33/40 = 0.825 and the false alarms F = 18/40 = 0.450; d′ = z(H) − z(F) = 1.060 [0.460, 1.661], and the p-value (< 0.001) is that of Fisher’s exact test, one-sided, that A samples receive more “A” answers. No proportion may be 0 or 1: with them the model has no finite estimate and the app gives no result.

Paired preference

With Prefer A (38), Prefer B (22) and No preference (5), the app runs a two-sided binomial test that half prefer each product. The “no preference” answers either are excluded (the default: 38 of 60, 63.3% [49.9, 75.4]%, p = 0.052) or are split half and half (40 of 64, 62.5% [49.5, 74.3]%, p = 0.060). Below the tiles, a note says what was done with them: if they are excluded, “"No preference" answers are left out of the test.”; if they are split and their number is odd, like the starting 5, “Odd number of "no preference" answers: one was left out when splitting them.” (two go to A, two to B and one is left out). With the starting values, the preference for A is not shown.

6.4Hedonic

The affective test par excellence: each consumer rates each product on the nine-point hedonic scale, from 1 “dislike extremely” to 9 “like extremely”. The app compares the products treating each consumer as a block.

The Consumer liking card asks for one row per consumer and product with three roles: Consumer, Product and Liking. The example, “Coffee: 80 consumers (liking, just-about-right and CATA)”, has 320 rows and 16 columns (consumidor, cafe, agrado, three jar_… columns and ten terms); only the first three are used here.

The tiles give the Consumers (80), the Products (4), the Product effect (F = 56.31, p < 0.001), the Most liked (Altura lavado, 6.51 · a) and the CV (21.1%). The reading turns the extreme means into words of the scale—6.51 is “like moderately”, 4.31 “dislike slightly”—rounding the mean to the nearest point. The Liking by product figure shows the mean of each product with its standard error and its letters.

The ANOVA is two-way without interaction, liking = mean + product + consumer + error: product (3 df, F = 56.31), consumer (79 df, F = 2.70) and error (237 df, MS 1.505). Removing the variation between consumers—some rate everything high, others everything low—is what makes the test sensitive. The table of means, downloaded as hedonic.csv, gives n, the mean, the SD, the SE (√(MS_error/n) = 0.137) and the Tukey–Kramer Group at 5%: Altura lavado 6.51 a, Honey 6.45 ab, Natural 5.99 b and Comercial 4.31 c. Products sharing a letter do not differ: Honey cannot be told apart from either Altura lavado or Natural, but these two do differ from each other.

Below, Rank alternative (Friedman) ranks the products within each consumer and compares the rank sums (χ² = 90.87, p < 0.001), with its own letters: Altura lavado and Honey a (mean rank 2.99), Natural b (2.61) and Comercial c (1.41). Use it if you do not accept that the hedonic scale is an interval scale, that is, that the distance from “like slightly” to “like moderately” is the same as from “moderately” to “very much”. Friedman only uses the consumers who rated every product.

6.5Just-about-right and penalties

Knowing that a coffee is liked less does not say what to change. Just-about-right (JAR) scales ask, for each attribute, whether it is “too little”, “just right” or “too much”, and penalty analysis counts how much liking is lost for each deviation.

The Just-about-right scales card asks for one row per consumer and product with Consumer, Product, Liking and the Just-about-right attributes, which the app proposes by itself from the columns whose name begins with jar_ (in the example, jar_acidez, jar_amargor and jar_cuerpo—acidity, bitterness and body; the prefix is dropped in the results). Below are two fields: Scale levels (5: 1 = too little, 3 = just right, 5 = too much) and Consumer threshold (%) (20). The scale must have a center: 3, 5, 7 or 9 levels. With an even number, the app warns, in a box below those two fields, “With an even number of levels there is no center: use 3, 5, 7 or 9.”, and hides the results (which also leave the Block 9 report) until you write an odd number; the loaded data are not lost.

The reading lists up to six penalties that matter, sorted by the weighted penalty, with the percentage, the drop and its p. The table (jar_penalties.csv) gives, by product and attribute, the % “low”, “JAR” and “high”, the two drops with their p and the larger of the two weighted penalties. In the Penalty plot, each label gives the product and the attribute in full, with “+” for too much and “−” for too little (“Comercial · amargor +”); the app places them so they do not overlap and, when a label has to move away from its point, joins them with a short leader line. The legend of the product colors goes outside the plot area, on the right, and the drop axis has ticks every half point (0, 0.5, 1 and 1.5 in the example); a negative drop (below zero) means that those off the just-right point rate higher. The second figure, Distribution of just-about-right answers, stacks the three percentages of each product and attribute, also with the full names.

The reading flags by percentage and drop, not by p-value: a penalty with p = 0.483 appears if it gathers 20% of the consumers. Check the p in the table before recommending a change.

6.6CATA

In the check-all-that-apply (CATA) question, the consumer checks, from a list of terms, those that describe each product. It is quick and needs no training; the app tells which terms separate the products and draws the map that relates them.

The Check all that apply card asks for one row per consumer and product, with Consumer, Product and Terms (0/1): the app proposes by itself the columns that contain only 0 and 1 (and at least one 1) and do not begin with jar_. In the example there are ten: Afrutado (fruity), Chocolate, Floral, Nuez (nutty), Tostado (roasted), Quemado (burnt), Ácido (acidic), Amargo (bitter), Dulce (sweet) and Astringente (astringent).

The tiles give the Complete consumers (80: those who evaluated every product, the only ones that enter the tests), the Terms (10), how many Discriminate products (10, by Cochran’s Q with p < 0.05) and the Inertia on the plane (94.6%, with the χ² of the table, 295.1). The reading names the discriminating terms and the three most checked in each product: Altura lavado, Afrutado 68%, Ácido 58% and Floral 43%; Comercial, Amargo 74%, Tostado 64% and Quemado 53%.

The table (cata.csv) gives the percentage of each term in each product, Q, its p and the Differing pairs (Holm); the rows of the discriminating terms are highlighted. The second figure, Frequency of each term, plots those percentages as grouped bars. A term can discriminate overall without any pair differing after the adjustment: this is the case of Chocolate (Q = 11.16, p = 0.011), between 25.0% in Comercial and 47.5% in Honey, whose pairs column says “—”. Dulce, in contrast, separates five of the six pairs.

6.7Descriptive profile

A trained panel rates the intensity of each attribute on a continuous scale, several times. It is the tool for describing precisely what a treatment changes: not whether it is liked, but how much more acidic, more bitter or fuller-bodied the product turns out.

The Trained panel card asks for one row per judge, product and session, with Judge, Product, Session or replicate (optional) and the Attributes. The example, “Coffee: quantitative descriptive profile” (64 rows, 10 columns), has eight judges who evaluate the four coffees in two sessions, with seven attributes from 0 to 10: Fragancia (fragrance), Acidez (acidity), Amargor (bitterness), Cuerpo (body), Dulzor (sweetness), Astringencia (astringency) and Residual (aftertaste). Its description warns of three weak judges: “Judge J6 was simulated with more noise (repeats poorly) and J8 with hardly any differences between coffees (barely discriminates); by chance, J4 also came out weak. The panel performance flags all three.” (Section 6.8). Mean comparison chooses between Fisher’s LSD (the default) and Tukey.

The tiles give the Judges (8), the Products (4), the Discriminating attributes (7 / 7, “product against the interaction”) and the variation retained by PCA: first two dimensions (97.3%). The table (descriptive_profile.csv) gives, by attribute, the product F against the interaction, its p and the mean of each product with its letters, computed with the same interaction error:

All p-values are < 0.001 except that of Cuerpo (0.002). With Tukey, which is stricter, two letters change: the bitterness of Altura lavado becomes “bc” and the body of Honey “ab”. The LSD protects little when there are many products; with four, the two usually agree.

The figures are the Sensory profile (spider chart), with one axis per attribute and one line per product, and the Product map (PCA of the means): the principal component analysis of the product × attribute table of means, with the products as points and the attributes as arrows (their correlation with the components, rescaled). In the example, PC1 (81.3%) sets Comercial against the other three, and PC2 (16.0%) separates the acidity of Altura lavado from the body of Natural. The Send to PCAPro (preference map) → button passes those means to PCAPro, of the same suite, as profile_product_means.csv, to cross them with consumer liking.

6.8Panel performance

A profile is only as good as its panel. The second card checks each judge with three questions: does the judge tell the products apart? Repeat the rating? Agree with the others?

For each judge and attribute, the app fits a one-way ANOVA with the judge’s own ratings (product, using the replicates) and summarizes the seven attributes in the table (panel_performance.csv):

The thresholds are lenient on purpose: with two sessions, the ANOVA of a single judge has very few degrees of freedom and little power. In the example, the reading says: “Consider retraining or checking: J4 (discriminates little, repeats poorly); J6 (discriminates little, repeats poorly); J8 (discriminates little). The least repeatable is J6 (mean residual SD 2.30).” J4 and J6 discriminate in no attribute (median p 0.268 and 0.460), and their residual SD (1.40 and 2.30) exceeds 1.5 times the panel median; J8 repeats well (0.60) and agrees with the panel (0.85), but discriminates in a single attribute. They are the three announced by the description of the example: J6 and J8 were simulated that way, and J4 came out weak by chance. All eight agree with the panel (median r between 0.84 and 0.97).

Detail of the attribute chooses an attribute and shows two tables: its full ANOVA and the performance of each judge in it. With Fragancia, the ANOVA gives Product F = 17.20 against the error, Judge 2.00 (p = 0.088), Session 0.75 (p = 0.393) and Product × judge 0.51 (p = 0.942); the F of 33.45 in Table 6.2 is the product MS (34.385) divided by that of the interaction (1.028). In the second table, J6 has the largest residual SD in Fragancia (3.19).

6.9Ballots

The last tab prepares the session: in what order each judge receives the samples, with which three-digit code, and the printed ballots on which to answer. A poorly balanced order brings into the results the effect of position and that of the previous sample.

Session design

The fields are in two rows: on top Test, Judges, Seed and Ballot title; below, wide so they can be read in full, Products (comma separated) and Attributes (profile).

Generate the plan builds the plan and enables the other two buttons. Print the ballots opens a window with one ballot per judge, on letter paper, and sends it to print: the hedonic ballot asks to mark the nine-point scale for each code, in the order shown, with the instruction to rinse between samples; the profile ballot, a line scale from “low” to “high” per attribute; the triangle ballot, to circle the code of the different sample. All carry the judge, a line for the date and another for comments. If the browser blocks the window, the app warns “The browser blocked the window: allow pop-ups to print.” ⤓ Serving plan (CSV) downloads serving_plan.csv, with the columns judge, position, product and code, one row per sample served.

The Serving plan card says so in the reading—“The plan is balanced: 12 judges is a multiple of the 4 orders.”, or, with 10 judges, “With 10 judges the balance is not complete: use a multiple of 4 (for instance 12).”—, shows the table with the code and product of each position for each judge (also downloadable as CSV and XLSX) and a preview of the first four ballots, with the codes only.

The block is called Postharvest trials (in the bar, Trials) and introduces itself as “Treatment × time factorials, repeated measures, slopes and randomization.” It has four tabs: Treatment × time factorial, Repeated measures, Slopes and Randomization.

The first three take a table in long format—one row per fruit and time, with the response, the treatment and the time in columns—and compute as soon as the table is loaded. The examples are two simulated data sets that already appeared in Chapters 2 and 3: the example mango at 13, 20 and 25 °C, which was sampled destructively (four new fruit were measured each day), and the example chayote with two coatings, whose eighteen tagged fruit were weighed every five days. The chayote treatments are named in the data as Testigo (control), Cera vegetal (vegetable wax) and Quitosano (chitosan), and the app shows them with those names.

7.1Treatment × time factorial

The Destructive sampling card explains it: “Each sampling time uses different fruit (destroyed when measured): the trial is a treatment × time factorial, completely randomized or in blocks.”

The roles are Response variable, Treatment, Time and Block (optional); with a block, the design is a randomized complete block design and the block enters the model as one more effect. Time is treated as a factor (each day is a level), not as a number: this lets the response change in any way over time. With the example mango the app picks firmeza_N, temperatura as the treatment and dia; you can switch the response to any other column of the table (sst, at, L…).

The analysis of variance

The app fits the model y_ijk = μ + τ_i + δ_j + (τδ)_ij + ε_ijk (plus the block, if there is one), with τ the treatment, δ the time and (τδ) their interaction (Steel et al. 1997). In the mango, the 13 °C temperature was measured up to day 21 and those of 20 and 25 °C only up to day 12; with the box checked, the reading warns “Times lacking some treatment were left out: 15, 18, 21.” and the analysis uses 60 fruit (3 temperatures × 5 days × 4 fruit).

The Analysis of variance card opens with five tiles—the F and p-value of the Treatment, the Time and the Interaction, the CV and the R²—and continues with the reading, the analysis table and the figure Course by treatment:

The CV is 10.3% and the R², 0.979. All three sources are significant, and the one that rules the reading is the interaction: “The interaction is significant (p < 0.001): the effect of temperatura changes with storage time, so treatments are compared within each time (table below), not by their overall averages.” The interaction tile turns amber when it is significant, as a warning.

When combinations are missing

If you untick “Use only the times measured in every treatment,” the analysis takes all the days and the factorial is left with empty cells: combinations of treatment and time without any fruit. In the mango there are six (20 and 25 °C lack days 15, 18 and 21), and the Analysis of variance card opens with a warning that names them and says what is lost:

“6 combinations of temperatura and dia have no data (20 × 15, 20 × 18, 20 × 21, 25 × 15, 25 × 18, 25 × 21). With empty cells, type III sums of squares cannot test the main effects of temperatura and dia: each would be averaged over cells that do not exist, so those rows are left without df, SS, MS, F or p. The interaction (with fewer degrees of freedom) and the comparisons within each time remain valid.”

With type III, the Treatment and Time tiles turn amber with “F = —” and not estimable (empty cells), and in the table those two rows say not estimable in the F column and carry dashes in df, SS, MS and p: without the hypothesis, what would remain after dropping the factor from the model is not the sum of squares of any effect. The interaction is tested, with 8 degrees of freedom instead of 14 (F = 23.03, p < 0.001), against an error of 38.610 with 54 df; the analysis uses the 72 fruit and the R² rises to 0.980. The table of means adds days 15, 18 and 21 with a dash for the temperatures that were not measured. At the foot of the warning, the app proposes the two ways out: “To test the main effects, tick ‘Use only the times measured in every treatment’ again or choose type I.”

With Type I (sequential) each effect is tested in order and all three have an F; the warning, now informative, explains it: “With type I each effect is tested in order (dia adjusted for temperatura) and the interaction loses 6 degrees of freedom.” In the mango, temperature gives F = 100.24 (2 df), day adjusted for temperature F = 320.65 (7 df) and the interaction the same F = 23.03, all with p < 0.001. Even so, the cleanest way to test the main effects is the default one: compare only the common times.

7.2Comparing treatments within each time

The table Treatments within each time has one row per time and one column per treatment, with the mean of each cell and its letters: “At each time, treatments sharing a letter do not differ.”

The comparisons use the error mean square of the full analysis (44.658 with 45 df in the mango), not only the fruit of that day, and the letters are assigned with the insert-and-absorb algorithm of Piepho (2004). Tukey uses the Tukey–Kramer version for cells of different size (Kramer 1956); Bonferroni divides α by the number of pairs; LSD corrects nothing and is recommended only when there are few treatments and the F was already significant.

With Dunnett (against the control), the letters are replaced by an asterisk next to each treatment that differs from the control (“* differs from the control (Dunnett, α = 0.05).”). With the mango and the control at 13 °C, 20 °C differs already from day 0 (129.43 versus 115.83 N) and 25 °C from day 3 (60.33 versus 107.65 N). Dunnett has more power than Tukey when all that matters is each treatment against the control (Dunnett 1955), as in a coating trial. The table is downloaded with ⤓ CSV and ⤓ XLSX (means_by_time).

7.3Repeated measures

The Repeated measures tab analyzes trials in which the same fruit are always measured. Its card, The same fruit over time, sums it up: “Weight, color or another non-destructive measure taken on the same fruit (units) at each time: a split plot in time, with the correction of the degrees of freedom when the measurements of a unit are not equally correlated.”

One role is added to those of the factorial: Unit (fruit), the identifier of each fruit, which must be repeated at all its times. The example is the weight loss of the chayote: 6 tagged fruit per treatment (control, vegetable wax and chitosan), weighed every 5 days up to day 25 (See the data (108 × 4)); the app picks perdida_peso, tratamiento, dia and fruto. The comparison controls are the same as in the factorial: Mean comparison, Control (Dunnett) (here, Testigo) and α.

Before analyzing, the app removes the times at which all units have the same value, because they carry no information; with weight loss this is day 0, when all fruit are at zero, and the reading warns about it: “Times at which every unit has the same value were left out (they carry no information): 0.” Units that lack some time are also left out, and the Units tile says how many.

Error a (2.6224) is fifteen times error b (0.1714): that is the reason for testing the treatment against the units, as its tile says, “p < 0.001 (against the units).” Even so, the treatment is significant (F = 18.09 with 2 and 15 df), as are time (F = 795.45) and the interaction (F = 16.49).

7.4Sphericity and corrections

The split-plot analysis assumes that all differences between two times of the same fruit have the same variance (sphericity). In storage this almost never holds: two consecutive weighings resemble each other more than the first and the last do.

The app checks the assumption with Mauchly’s test (1940) and computes two correction factors, the epsilons of Greenhouse–Geisser (1959) and Huynh–Feldt (1976, with the correction of Lecoutre 1991). An ε of 1 indicates perfect sphericity; the smallest possible is 1/(t − 1), with t times. The degrees of freedom of time and of the interaction are multiplied by ε, and their p-values are recomputed with them: the columns p (GG) and p (HF) of the table.

With the chayote, Mauchly rejects sphericity (p < 0.001) and the epsilons are 0.280 (GG) and 0.286 (HF), close to the minimum of 0.25 for five times: the correlation between weighings is very uneven, as expected for a cumulative loss. The reading says so: “Mauchly’s test rejects sphericity (p < 0.001), so read the Greenhouse–Geisser (ε = 0.280) or Huynh–Feldt corrected p-values.” Even after correction, time and the interaction remain significant (p < 0.001), and the reading refers you to the Slopes tab to compare the rates.

The treatments within each time

The table of means by time is the same as in the factorial, with one difference that the app notes at the foot: “Within each time the pooled error of the two strata is used, with Satterthwaite degrees of freedom.” Comparing treatments on a fixed day mixes the variation among fruit and that within each fruit, so the error is the combination (Ea + (t − 1)·Eb)/t, with degrees of freedom approximated by the Satterthwaite method (1946).

With Dunnett against the control, vegetable wax and chitosan differ from the control from day 10 on (asterisk) and not on day 5. The methods cited are Steel et al. (1997), Greenhouse and Geisser (1959), Huynh and Feldt (1976), Lecoutre (1991), Mauchly (1940) and Satterthwaite (1946).

7.5Slopes

When the attribute changes almost linearly with time, the most direct way to compare treatments is to compare their rates. The Slopes tab, with the card Rate of change by treatment, fits “A straight line of the attribute against time for each treatment and the test of whether the slopes (the rates) are equal: analysis of covariance.”

The roles are Attribute, Time (numeric)—here time is indeed a number—and Treatment. The example is again the weight loss of the chayote, now with day 0 included (the lines start from zero). The card Lines and comparison of slopes gives three tiles: Equal slopes (the F of the test), Fastest and Slowest.

With the chayote, the rates differ (F = 39.05, p < 0.001): the control loses 0.4473% of its weight per day, vegetable wax 0.2924% and chitosan 0.3078%. The reading sums it up: “Testigo changes 1.53 times faster than Cera vegetal.” The pairs with Holm confirm what the table of means showed: the control differs from both coatings (p < 0.001 in both pairs) and vegetable wax and chitosan do not differ from each other (difference −0.01536% per day, p = 0.428). Significant rows are shaded green.

7.6Randomization and field book

The Randomization tab is used before the trial: “Generates the random assignment of treatments (and sampling times) to the units, with a seed to repeat it.” Its card is Field book of the trial.

The Generate button randomizes and shows the Field book card, with three tiles (Units, Measurements and Design) and the table, of which up to 300 rows are shown. With the preset values, destructive sampling gives 60 units and 60 measurements (3 treatments × 5 times × 4 replicates, each fruit measured once); with the repeated-measures box, 12 units and 60 measurements (each of the 12 fruit, 3 × 4, is measured at the 5 times).

The columns are Plot, Replicate (or Block in complete blocks), Treatment, Time and the variables to measure. In blocks, plots are numbered by block (101, 102… in block 1). In repeated measures, each plot appears in as many rows as there are times, already sorted: that way each fruit is weighed on its date. ⤓ CSV and ⤓ XLSX download the whole book (field_book), and Open the experimental-design app → opens, in another tab, the experimental-design program of the LABG suite, whose data block recognizes those columns. Once measured, the same file with the columns filled in is loaded in the Treatment × time factorial tab or in Repeated measures (with Plot as the unit).

Block 8 is subtitled “Loads, venting, room environment, costs, compatibility and units.” It has six tabs: Pallet and container, Box venting, Store environment, Storage cost, Compatibility and Units. None reads a data table: all open with example values written in their fields and recompute as soon as you change one, so there is no example to load. The figures in this chapter are those of the starting values.

8.1Pallet and container

A box that does not fill the pallet well wastes space in every layer, every pallet and every container; a box that overhangs gets crushed. The tab looks for the best arrangement of the boxes on the pallet and of the pallets in the container.

The Boxes per pallet card has two groups of fields. The pallet: Pallet (ISO 120 × 100 cm, European 120 × 80 cm, North American 121.9 × 101.6 cm (48 × 40 in) or Other size), which fills Pallet length (cm), Pallet width (cm) and Pallet height (cm); if you change a dimension by hand, the selector switches to Other size. The box and the limits: Box length (cm) 40, Box width (cm) 30, Box height (cm) 20, Full box weight (kg) 10, Maximum load height (cm) 210 (including the pallet), Maximum load weight per pallet (kg) 1000—the produce with its boxes, without the pallet—and Empty pallet weight (kg) 25, that of a wooden pallet; a plastic one or one of another size weighs differently, and this weight only counts in the container.

The pallet tiles are Boxes per layer (with the area it uses), Layers (with what limits them: “limited by height” or “limited by weight”), Boxes per pallet and Load weight, with the total height. The One layer seen from above plot draws the arrangement, with one color per block. In the example, nine 20 cm layers on a 15 cm pallet add up to 195 cm, below the 210; a tenth would exceed the limit. With the European 120 × 80 cm pallet, 8 boxes fit per layer and 72 per pallet.

Pallets per container

Below, Container chooses among 20 ft reefer, 40 ft high-cube reefer and 53 ft refrigerated trailer, with their indicative inside dimensions and payload, and the Stack pallets (two tiers if they fit) box puts one pallet on top of another if the container height allows it. The app arranges the pallets on the floor with the same method as the boxes and limits their number by the payload, adding to each pallet the Empty pallet weight (kg). The tiles are Pallets per container, Boxes per container, Payload—the produce and boxes plus the empty pallets, as it explains below: “produce and boxes, plus 25 kg per empty pallet”; in the 40 ft container, 20 × (900 + 25) = 18,500 kg—and Floor used, and the Container floor plot draws the arrangement.

With 195 cm pallets, checking Stack pallets changes nothing: two do not fit in the 255 cm of the 40 ft container. The reading reminds you that a use below 85% suggests changing the box size, that boxes must not overhang the pallet, and that air channels must be left. Container dimensions vary with the make: “check the carrier’s sheet.”

8.2Box venting

In forced-air cooling, the air has to pass through the boxes. If the faces where it enters and leaves have little open area, cooling takes longer; if they have too much, the box loses strength and is crushed in the stack.

The Open area of the faces card asks for the dimensions of the two faces—Long face: length (cm) 50, Long face: height (cm) 25, Short face: width (cm) 30 and Short face: height (cm) 25—and an editable table of holes with Face (Long or Short), Shape (Rounded slot, Rectangle or Circle), Length or diameter (cm), Width (cm) and Count. The area of a rounded slot of length a and width b is (a − b)·b + πb²/4; that of a circle, πa²/4. The result is the area of the holes on each face over the area of the face, in %.

8.3Store environment

The temperature and relative humidity of the room decide how much water the produce loses. What drives it is the vapor pressure deficit between the surface of the produce, saturated at its own temperature, and the surrounding air.

The Air, produce and water loss card has eight fields, with these starting values: Air temperature (°C) 5, Relative humidity (%) 85, Altitude (m) 0, Produce temperature (°C) 6, Produce (transpiration coefficient) Tomato · 140, Coefficient (mg kg⁻¹ s⁻¹ MPa⁻¹) 140, Outside air (°C) 28 and Outside RH (%) 55. The produce selector has fourteen indicative coefficients from Sastry et al. (1978), from apple (42) to lettuce (7400); if you type another coefficient, the selector switches to Other (type it).

The tiles give the state of the room air (ASHRAE 2017): the Pressure, which comes from the altitude; the Absolute humidity in g/m³, with the humidity ratio in g per kg of dry air; the Dew point, the Wet bulb and the Enthalpy; the Air deficit and the Produce–air deficit; and the Water loss per day and per week. The saturation pressure comes from the equations of Wagner and Pruss (2002) over water and of Wagner et al. (2011) over ice, the same ones used in the 2017 tables.

8.4The psychrometric chart and water loss

The psychrometric chart puts the temperature and the water content of the air in a single figure. It shows at a glance how far the room air is from saturation and what happens to outside air when it comes in.

The Psychrometric chart plot is drawn at the site pressure, so it changes with altitude, and its temperature axis runs from −2 °C to 35 °C, extended if the room is below 1 °C or the outside air above 32 °C, to leave a 3 °C margin. The vertical distance between the room point and the saturation curve is the water the air can still take up. The outside air in the example carries almost three times more water per kilogram than the room air: when it comes in through an open door and cools to 5 °C, it passes its dew point and condenses on the evaporators, which is part of the “other loads” of Section 4.7. Each curve carries its RH percentage on the right edge, at the height of its end.

A water loss of 3 to 5% of the weight already shows as wilting or shriveling in many products; the loss tile turns amber when it exceeds 3% per week. The transpiration coefficient varies almost two hundredfold between products: the lettuce in the selector loses water fifty times faster than tomato in the same room.

8.5Storage cost

Keeping produce in cold storage to sell it later only pays if the price rises more than each day of waiting costs. The tab computes that daily cost per pallet, shrinkage included.

The Cost per day and per pallet card asks for Energy (kWh per day) 180, Tariff per kWh 2.8, Labor per day 900, Other costs per day 250, Depreciation and rent per year 420,000, Capacity (pallets) 60, Occupancy (%) 75, Shrink per day (% of weight) 0.08 and Value of one pallet 18,000. Amounts of money are in whatever currency you use; the app writes no symbol.

Occupancy weighs heavily: with the room full (100%) the operating cost falls to 46.74 per pallet and the total to 61.14, because the fixed costs are spread over more pallets. Shrinkage, on the other hand, does not depend on occupancy: it depends on the humidity and temperature of the room (Section 8.3).

8.6Compatibility

In practice many products share a room or a container. It is not always possible: one needs a temperature that causes chilling injury to the other, one produces the ethylene that ripens or yellows the other, or one gives off odors the other absorbs.

The Can they share the room? card shows a button for each of the 38 products in the table; a click selects or deselects it (the selected ones are highlighted). At the start, green banana, apple, lettuce and carrot are selected. The Table of products (editable) drop-down holds, for each product, the recommended temperature and RH (T min (°C), T max (°C), RH min, RH max), the ethylene production class at 20 °C (Ethylene: VL < 0.1, L 0.1–1, M 1–10, H 10–100 and VH > 100 µL kg⁻¹ h⁻¹), the ethylene Sensitivity (L, M, H), Chilling injury (0 none, 1 moderate, 2 sensitive) and Odor (“p” gives off, “a” absorbs). These are indicative values for the most common cultivars (Kader 2002; Gross et al. 2016; McGregor 1989): correct them with those of your cultivar or add products with + Add row.

The Diagnosis card appears when at least two products are selected. Its tiles are Products, Incompatible pairs, Pairs at risk, Shared temperature and Shared RH (the range all of them share, or “none”). The reading lists each problem, pair by pair. A pair can be incompatible and also carry a risk: each tile counts all the pairs with that kind of problem, the same ones the list names, and the pairs-at-risk tile says below how many are also incompatible. In the example, “Pairs at risk: 3 · 3 also incompatible”: the three “Ethylene risk” items on the list are in pairs that were already incompatible. The shared temperature and RH are written as in the list, with a true minus sign and “to” between the ends when one is negative.

8.7Units

Data sheets, papers and equipment use different units: degrees Fahrenheit, pounds-force, thousandths of an inch, parts per million. The last tab converts them.

The Unit conversion card has three controls: Quantity, Value (40) and From, the unit of the value. The results appear in tiles, one for each other unit of the quantity, with six significant figures.

Two conversions come up often in postharvest work: the firmness a penetrometer gives in kgf or lbf (1 kgf = 9.807 N; 1 lbf = 4.448 N) and the thickness of films, which many suppliers give in mil, thousandths of an inch (1 mil = 25.4 µm: a 40 µm film is 1.57 mil). In concentration, ppm and µL/L are the same thing, which is why the list names them together, “ppm (µL/L),” like ppb and nL/L.

Reading the block’s results

The block subtitle says what it does: Everything you computed, in a document to share; and your work, in a file to continue later. It has no tabs, but four cards, one below the other: The report, Handling recommendations, Project and How to cite PostHarvestPro.

9.1Report details and sections

Every analysis you run in Blocks 2 to 8 leaves a section ready for the report. The The report card lets you write the cover, choose which sections go in and generate the document.

Its hint sums it up: It gathers the sections the blocks left, with their charts (SVG, in the light-theme colors), tables, interpretation, handling recommendations, methods and references. It is a single HTML file that opens in any browser and prints to PDF. The cover fields are:

Available sections lists one check box per section, with its name and its block (· Block 2…), in block order. There are up to 27, one for each analysis that leaves results:

The list has two parts. At the top, ticked, the sections you used: those of the tools where you loaded data, edited a table or changed a setting. Below, unticked and under the label With the example values the tool opens with (you have not used them; tick them if you want them in):, those that only have the starting values. The tools that open with typed values compute from the moment the app opens and therefore leave their section without your touching them: Temperature dependence, Accelerated test, Respiration (flow-through), Modified atmosphere, Precooling and heat load, Losses along the chain, Improvement what-if, Discrimination tests and the three of Block 8, eleven in all. When the app opens, they are all at the bottom and the top says No sections yet: run some analysis in Blocks 2 to 8.; as soon as you work in one of those tools, its section moves up and is ticked by itself.

You can tick or untick any of them: the report carries exactly the ticked ones, and the app remembers your choice even if the list is rebuilt when another analysis runs. The one-off calculators—acidity, moisture, firmness and weight loss in Block 2, venting, cost and units in Block 8—leave no section.

9.2Generate, download and print

Below the sections there are three buttons, and one last step remains before sharing:

1. Generate the report. Assembles the document with the ticked sections and shows it in a preview inside the same card; a notice confirms Report ready. If you ticked none, the app says so: Pick at least one section (or run some analysis). If you later change something in another block, press it again: the preview does not update by itself.
2. ⤓ Download HTML. Saves the report as postharvestpro_report.html. It is a single file, with the figures inside as SVG, that opens offline in any browser and can be sent by email.
3. Print or save PDF. Opens the browser’s print dialog on the preview. For a PDF, choose Save as PDF as the destination.
4. Check before sharing. The report comes out in the language of the interface at the moment it is generated; change the language with ES · EN and generate it again if you need it in Spanish. The figures are written with the light-theme colors even if you work in the dark one, and the report’s style sheet has print margins and avoids splitting a figure across two pages.

9.3What the report contains

The document always has the same structure:

References are chosen by block, not by section: if you include only Quality summary, the report lists the six methods of Block 2 and their works, even if you did not use the scales or the size grades.

9.4Handling recommendations

The second card turns the results into practical recommendations: They come from the results of the sections ticked above, through explicit rules; check them with your own judgment before using them. They are redone every time a block changes a result or you tick or untick a section, and they are the same ones that go into the report.

Each recommendation comes from a fixed rule applied to the result of a section, and it is only written if that section is ticked (the one about boxes, which leaves no section, if you worked in Block 8›Box venting). The table says which; the last column gives what the app writes with the examples loaded.

With no sections ticked—for instance, when the app opens—, the card says There are no results yet to draw recommendations from.; in the report, if no ticked section yields a recommendation, the recommendations part reads No automatic recommendations for these sections.

9.5The figures, the studio and the editor

The figures of the report are the same as those of the app. If you need them separately—for a thesis, an article or a presentation—, each one is downloaded from its box, and polished in the figure studio or in its editor.

In the corner of each figure there are two quick downloads: Download SVG, a vector that can be edited in any drawing program, and Download PNG at 300 ppi, an image 170 mm wide—that of a journal page—with its resolution written into the file. Both use the light-theme colors. Many figures also have Figure data (CSV), with the numbers that were drawn. When you hover over the figure two more buttons appear: ✎ (Edit this figure: titles, axes, series, legend, texts and annotations) and the one with the pencil and ruler (Open in the figure studio: split screen to edit and export). The Ctrl + K search also finds figures by their title and opens them in the studio.

The studio is shared by the whole suite. It puts the figure on the left, to scale, and the inspector on the right. The top bar undoes and redoes, compares before and now, zooms in and out (Fit sizes it to the screen), shows a ruler, applies one-click Presets and exports with Export; other buttons arrange the inspector and Close studio goes back to the app. The inspector begins with Search a control… and has these sections:

The studio’s footer recalls the shortcuts: Click the figure: its section · Double-click a text: change it · Ctrl + wheel: zoom · B: before and now · ?: shortcuts. Changes in the studio and the editor only affect how the figure looks, never the data or the computations.

9.6Saving and opening the project

The app does not keep your data from one session to the next: every time you open it, it starts empty. The Project card solves that: Saves into a JSON file the tables you loaded, the columns you chose, the edited tables and the settings. When you open it, the app recomputes everything. The file stays on your computer.

• ⤓ Save project downloads postharvestpro_project_date.json with the tables of every tool that read data (with the role of each column), all the editable tables (scales, size grades, chain, films, products…), the value of every field and every selector in Blocks 2 to 8, the language, the report cover details and which sections you used and which ones you ticked or unticked.
• Open project… reads that file, puts each value back in its place, runs all the analyses again and leaves the same sections ticked as when it was saved. When it finishes it says how much it restored: Project opened: … data tables, edited tables and settings. If the file is not from the app, it warns: The file is not valid JSON. or The file is not a PostHarvestPro project.

There is no keyboard shortcut for saving: it is done with the button. The project does not save the figures or the report, which are redone when it is opened. If you had already worked when you close the tab, the app warns you that you will lose what you did not save.

9.7How to cite PostHarvestPro

The last card repeats the citation of the home page (Section 1.8), without copy buttons: the reference in the language of the interface and the BibTeX entry.

The BibTeX entry has the key barreraguzman2026postharvestpro, the English title, the version, the year, the license GPL-3.0-or-later, the DOI and the address. The citation carries the Zenodo concept DOI, which always resolves to the latest version. Also cite the method of each result, given by its Method and source: line and by the Methods and references section of the report.

AThe files the app reads and writes

PostHarvestPro runs in the browser and sends nothing to any server: the tables come in from your computer and what the app writes goes out to your downloads folder.

A.1 · What the app reads

Every tool that analyzes a table has the same data entry (Section 2.1): Open file (CSV, TXT, XLSX, ODS), Paste a table or dropping the file on …or drop the file here. The project comes in through Block 9.

In every case the first row holds the column names (a column without a name is called col1, col2…, and a repeated name receives _2). A cell is a number if it looks like one (with sign, decimals or exponent); otherwise it is text. Empty cells, NA, N/A, NaN, null, - and — are missing. Tables are always in long format: one row per observed unit (fruit, jar, consumer by product) and one column per variable.

After reading the table, the app proposes the column for each role by its name: it compares ignoring case, accents and signs, first the whole name and then as part of the name (Temperatura (°C) works for the temperature), in Spanish or in English. Roles marked (optional) may be left at — none —. Some lists are proposed by their content: the CATA terms are the columns with only 0 and 1, and the just-about-right attributes, those beginning with jar_. In Block 5›Mechanical damage, volumen_mm3 and energia_J fill Bruise volume (mm³), for the susceptibility and Impact energy (J), and the mass (Fruit mass (g), if there is no energy) is used only when there is no energy. In Block 4›Climacteric, the column name also proposes the units: Time unit (days or hours; dia gives days and a name ending in _h, hours) and Respiration unit (mg or mL CO₂ kg⁻¹ h⁻¹, depending on whether it contains mg or ml).

The ten example datasets

The same ones the app carries, in the data/ folder and through ⤓ Example CSV in each tool. All are simulated (tools/generar_datos.R, seed 20261004), with their file and column names in Spanish in both languages.

An example of a long-format table, the mango one (the header and the first two rows):

"temperatura","dia","fruto","peso_inicial_g","firmeza_N","L","a","b","sst","at","ph","perdida_peso","antracnosis"
13,0,1,346,106.9,60.8,-11.2,34.1,8.9,1.28,2.99,0,0
13,0,2,294,128.7,61,-12.4,37,8.8,1.24,2.95,0,0

A.2 · What the app writes

With the English interface, the downloads are named in English; the table below gives those names (with the Spanish interface the same files are named in Spanish, as in the Spanish edition of this manual).

All CSV files use the comma as separator, the decimal point and Windows line breaks, and are in UTF-8 with a byte order mark so that a spreadsheet reads accents, the µ and the °. Result tables are written as they are seen: with the headers in the active language of the interface only (English with the English interface), the numbers already rounded and the intervals inside the same cell (0.500 [0.342, 0.658]); the sheet of the XLSX file carries the same name as the file. They are for reading or pasting into a document, not for computing again. The files that go to another app (the chain, the profile means, the serving plan, the field book) carry the full numbers.

BThe rules and formulas, gathered

The formulas the app computes and the rules with which it warns, classifies or decides, with the block where they act and their default values. They are the ones each chapter explains; here they are together for consultation at a glance.

B.1 · Quality, ripeness and color (Block 2)

B.2 · Kinetics, shelf life and rejection (Block 3)

B.3 · Respiration, ethylene and atmospheres (Block 4)

B.4 · Losses and mechanical damage (Block 5)

B.5 · Sensory evaluation (Block 6)

B.6 · Trials (Block 7)

B.7 · Packaging and storage (Block 8) and report (Block 9)

CGlossary

The postharvest, sensory and statistical terms the manual uses, in the sense in which the app uses them.

DWhen something does not work

The messages of the app, as they appear with the English interface, with what they usually mean and what to do. The ellipses stand for the part of the message that changes (a name, a number).

If the app goes blank or a card does not respond, reload the page: the data are lost, but the saved project is not. If the problem persists, open the app with Open PostHarvestPro.bat instead of double-clicking index.html.

EThe tool: license and how to cite it

E.1 · What it is and what it is not

PostHarvestPro is written for this program: the spreadsheet reader, the kinetic and survival models, the statistics, the psychrometrics, the figures, the report and the illustrations are in its own code, which can be read. It uses no third-party computing libraries, ships no typefaces (it uses the computer’s fonts), has no minified code or build steps and loads nothing from the network: that is why it opens with a double click and without a connection. The only links to the outside—the suite portal and the apps to which tables are sent—are followed only if you click them.

The only third-party elements are the line icons of the suite’s common modules (the block navigator, the figure studio and the animations button), taken from the Lucide project under the ISC license (and MIT for those Lucide inherited from the Feather project), both permissive and compatible with the GPL; the file LICENSES-TERCEROS.md, in the program folder, lists them with the text of their licenses. The example data are simulated (Appendix A). The app implements published methods, each one cited to its original source in the code, at the foot of each result, on the app’s home page and in the methods of the report (Appendix F).

E.2 · License

PostHarvestPro is distributed under the GNU General Public License, version 3 or later (GPL-3.0-or-later). The full text is in the LICENSE file, in the program folder.

E.3 · How to cite it

The How to cite section of the app’s home page gives the citation ready to copy, with Copy the citation and Copy BibTeX; the How to cite PostHarvestPro card in Block 9 shows the same two.

@software{barreraguzman2026postharvestpro,
  author  = {Barrera-Guzmán, Luis Ángel},
  title   = {PostHarvestPro: postharvest physiology and technology, quality, shelf life and sensory evaluation in the browser},
  version = {1.0.0},
  year    = {2026},
  license = {GPL-3.0-or-later},
  doi     = {10.5281/zenodo.23935616},
  url     = {https://doi.org/10.5281/zenodo.23935616}
}

Both citations carry the Zenodo concept DOI, which always resolves to the latest version; version 1.0.0 also has its own, 10.5281/zenodo.23935617.

Also cite, in your methods, the works behind the methods you used. The methods of the report (Chapter 9) already cite them by author and year, and its references section gives the full entries for the blocks you used.

FReferences

The 81 works in the app’s catalog, grouped by the first block that cites them and, within each topic, in alphabetical order. They are the same as in the References section of the home page and of the report.

F.1 · Quality, ripeness and color

• AOAC International. (2019). Method 942.15: Acidity (titratable) of fruit products. In Official methods of analysis (21st ed.).
• CIE. (2018). Colorimetry (4th ed., CIE 015:2018). Commission Internationale de l'Éclairage.
• Francis, F. J., & Clydesdale, F. M. (1975). Food colorimetry: Theory and applications. AVI Publishing.
• Hobson, G. E., Adams, P., & Dixon, T. J. (1983). Assessing the colour of tomato fruit during ripening. Journal of the Science of Food and Agriculture, 34(3), 286–292.
• Jiménez-Cuesta, M., Cuquerella, J., & Martínez-Jávega, J. M. (1981). Determination of a color index for citrus fruit degreening. Proceedings of the International Society of Citriculture, 2, 750–753.
• Jordan, R. B., Seelye, R. J., & McGlone, V. A. (2001). A sensory-based alternative to Brix/acid ratio. Food Technology, 55(4), 36–44.
• Judd, D. B., & Wyszecki, G. (1975). Color in business, science, and industry (3rd ed.). Wiley.
• Kader, A. A. (Ed.). (2002). Postharvest technology of horticultural crops (3rd ed., Publication 3311). University of California, Agriculture and Natural Resources.
• McGuire, R. G. (1992). Reporting of objective color measurements. HortScience, 27(12), 1254–1255.
• McKinney, H. H. (1923). Influence of soil temperature and moisture on infection of wheat seedlings by Helminthosporium sativum. Journal of Agricultural Research, 26, 195–218.
• Mokrzycki, W. S., & Tatol, M. (2011). Colour difference ΔE – a survey. Machine Graphics and Vision, 20(4), 383–411.
• Palou, E., López-Malo, A., Barbosa-Cánovas, G. V., Welti-Chanes, J., & Swanson, B. G. (1999). Polyphenoloxidase activity and color of blanched and high hydrostatic pressure treated banana puree. Journal of Food Science, 64(1), 42–45.
• Sharma, G., Wu, W., & Dalal, E. N. (2005). The CIEDE2000 color-difference formula: Implementation notes, supplementary test data, and mathematical observations. Color Research & Application, 30(1), 21–30.

F.2 · Kinetics, shelf life and time to rejection

• Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
• Arrhenius, S. (1889). Über die Reaktionsgeschwindigkeit bei der Inversion von Rohrzucker durch Säuren. Zeitschrift für Physikalische Chemie, 4, 226–248.
• Bates, D. M., & Watts, D. G. (1988). Nonlinear regression analysis and its applications. Wiley.
• Burnham, K. P., & Anderson, D. R. (2002). Model selection and multimodel inference (2nd ed.). Springer.
• Greenwood, M. (1926). The natural duration of cancer. Reports on Public Health and Medical Subjects, 33, 1–26.
• Hough, G., Langohr, K., Gómez, G., & Curia, A. (2003). Survival analysis applied to sensory shelf life of foods. Journal of Food Science, 68(1), 359–362.
• Kaplan, E. L., & Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457–481.
• Labuza, T. P. (1984). Application of chemical kinetics to deterioration of foods. Journal of Chemical Education, 61(4), 348–358.
• Lawless, J. F. (2003). Statistical models and methods for lifetime data (2nd ed.). Wiley.
• Mantel, N. (1966). Evaluation of survival data and two new rank order statistics arising in its consideration. Cancer Chemotherapy Reports, 50(3), 163–170.
• Marquardt, D. W. (1963). An algorithm for least-squares estimation of nonlinear parameters. Journal of the Society for Industrial and Applied Mathematics, 11(2), 431–441.
• Mizrahi, S. (2004). Accelerated shelf-life tests. In R. Steele (Ed.), Understanding and measuring the shelf-life of food (pp. 317–339). Woodhead.
• Ratkowsky, D. A., Olley, J., McMeekin, T. A., & Ball, A. (1982). Relationship between temperature and growth rate of bacterial cultures. Journal of Bacteriology, 149(1), 1–5.
• Taoukis, P. S., & Labuza, T. P. (1989). Applicability of time-temperature indicators as shelf life monitors of food products. Journal of Food Science, 54(4), 783–788.
• van Boekel, M. A. J. S. (2008). Kinetic modeling of food quality: A critical review. Comprehensive Reviews in Food Science and Food Safety, 7(1), 144–158.

F.3 · Respiration, ethylene, atmospheres and cooling

• Biale, J. B. (1964). Growth, maturation, and senescence in fruits. Science, 146(3646), 880–888.
• Exama, A., Arul, J., Lencki, R. W., Lee, L. Z., & Toupin, C. (1993). Suitability of plastic films for modified atmosphere packaging of fruits and vegetables. Journal of Food Science, 58(6), 1365–1370.
• Fishman, S., Rodov, V., & Ben-Yehoshua, S. (1996). Mathematical model for perforation effect on oxygen and water vapor dynamics in modified-atmosphere packages. Journal of Food Science, 61(5), 956–961.
• Fonseca, S. C., Oliveira, F. A. R., & Brecht, J. K. (2002). Modelling respiration rate of fresh fruits and vegetables for modified atmosphere packages: A review. Journal of Food Engineering, 52(2), 99–119.
• Lee, D. S., Haggar, P. E., Lee, J., & Yam, K. L. (1991). Model for fresh produce respiration in modified atmospheres based on principles of enzyme kinetics. Journal of Food Science, 56(6), 1580–1585.
• Lelièvre, J.-M., Latché, A., Jones, B., Bouzayen, M., & Pech, J.-C. (1997). Ethylene and fruit ripening. Physiologia Plantarum, 101(4), 727–739.
• Mangaraj, S., Goswami, T. K., & Mahajan, P. V. (2009). Applications of plastic films for modified atmosphere packaging of fruits and vegetables: A review. Food Engineering Reviews, 1(2), 133–158.
• Saltveit, M. E. (2016). Respiratory metabolism. In K. C. Gross, C. Y. Wang, & M. Saltveit (Eds.), Agriculture Handbook 66 (pp. 68–75). USDA.
• Siebel, J. E. (1892). Specific heat of various products. Ice and Refrigeration, 2, 256–257.
• Thompson, J. F., Mitchell, F. G., Rumsey, T. R., Kasmire, R. F., & Crisosto, C. H. (2008). Commercial cooling of fruits, vegetables, and flowers (Publication 21567). University of California, Agriculture and Natural Resources.

F.4 · Losses and mechanical damage

• Bajema, R. W., & Hyde, G. M. (1998). Instrumented pendulum for impact characterization of whole fruit and vegetable specimens. Transactions of the ASAE, 41(5), 1399–1405.
• FAO. (2019). The state of food and agriculture 2019: Moving forward on food loss and waste reduction. FAO.
• Finney, D. J. (1971). Probit analysis (3rd ed.). Cambridge University Press.
• La Gra, J., Kitinoja, L., & Alpuche, K. (2016). Commodity systems assessment methodology for value chain problem and project identification. IICA.
• Mohsenin, N. N. (1986). Physical properties of plant and animal materials (2nd ed.). Gordon and Breach.

F.5 · Sensory evaluation

• Bi, J. (2006). Sensory discrimination tests and measurements: Statistical principles, procedures and tables. Blackwell.
• Brockhoff, P. B., & Christensen, R. H. B. (2010). Thurstonian models for sensory discrimination tests as generalized linear models. Food Quality and Preference, 21(3), 330–338.
• Clopper, C. J., & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4), 404–413.
• Cochran, W. G. (1950). The comparison of percentages in matched samples. Biometrika, 37(3–4), 256–266.
• Ennis, D. M. (1993). The power of sensory discrimination methods. Journal of Sensory Studies, 8(4), 353–370.
• Ennis, J. M., & Jesionka, V. (2011). The power of sensory discrimination methods revisited. Journal of Sensory Studies, 26(5), 371–382.
• Friedman, M. (1937). The use of ranks to avoid the assumption of normality implicit in the analysis of variance. Journal of the American Statistical Association, 32(200), 675–701.
• Greenacre, M. (2007). Correspondence analysis in practice (2nd ed.). Chapman & Hall/CRC.
• Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer.
• Lawless, H. T., & Heymann, H. (2010). Sensory evaluation of food: Principles and practices (2nd ed.). Springer.
• MacFie, H. J. H., Bratchell, N., Greenhoff, K., & Vallis, L. V. (1989). Designs to balance the effect of order of presentation and first-order carry-over effects in hall tests. Journal of Sensory Studies, 4(2), 129–148.
• McNemar, Q. (1947). Note on the sampling error of the difference between correlated proportions or percentages. Psychometrika, 12(2), 153–157.
• Meyners, M., Castura, J. C., & Carr, B. T. (2013). Existing and new approaches for the analysis of CATA data. Food Quality and Preference, 30(2), 309–319.
• Næs, T., Brockhoff, P. B., & Tomic, O. (2010). Statistics for sensory and consumer science. Wiley.
• Peryam, D. R., & Pilgrim, F. J. (1957). Hedonic scale method of measuring food preferences. Food Technology, 11(9), 9–14.
• Stone, H., Sidel, J., Oliver, S., Woolsey, A., & Singleton, R. C. (1974). Sensory evaluation by quantitative descriptive analysis. Food Technology, 28(11), 24–34.
• Williams, E. J. (1949). Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Scientific Research, Series A, 2(2), 149–168.
• Xiong, R., & Meullenet, J.-F. (2006). A PLS dummy variable approach to assess the impact of jar attributes on consumer acceptance. Food Quality and Preference, 17(3–4), 188–198.

F.6 · Design and analysis of trials

• Copenhaver, M. D., & Holland, B. (1988). Computation of the distribution of the maximum studentized range statistic with application to multiple significance testing of simple effects. Journal of Statistical Computation and Simulation, 30(1), 1–15.
• Dunnett, C. W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association, 50(272), 1096–1121.
• Greenhouse, S. W., & Geisser, S. (1959). On methods in the analysis of profile data. Psychometrika, 24(2), 95–112.
• Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6(2), 65–70.
• Huynh, H., & Feldt, L. S. (1976). Estimation of the Box correction for degrees of freedom from sample data in randomized block and split-plot designs. Journal of Educational Statistics, 1(1), 69–82.
• Kramer, C. Y. (1956). Extension of multiple range tests to group means with unequal numbers of replications. Biometrics, 12(3), 307–310.
• Lecoutre, B. (1991). A correction for the ε̃ approximate test in repeated measures designs with two or more independent groups. Journal of Educational Statistics, 16(4), 371–372.
• Mauchly, J. W. (1940). Significance test for sphericity of a normal n-variate distribution. The Annals of Mathematical Statistics, 11(2), 204–209.
• Piepho, H.-P. (2004). An algorithm for a letter-based representation of all-pairwise comparisons. Journal of Computational and Graphical Statistics, 13(2), 456–466.
• Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2(6), 110–114.
• Snedecor, G. W., & Cochran, W. G. (1989). Statistical methods (8th ed.). Iowa State University Press.
• Steel, R. G. D., Torrie, J. H., & Dickey, D. A. (1997). Principles and procedures of statistics: A biometrical approach (3rd ed.). McGraw-Hill.

F.7 · Packaging, storage and psychrometrics

• ASHRAE. (2017). Psychrometrics. In ASHRAE handbook — Fundamentals (ch. 1). ASHRAE.
• Gross, K. C., Wang, C. Y., & Saltveit, M. (Eds.). (2016). The commercial storage of fruits, vegetables, and florist and nursery stocks (Agriculture Handbook 66). USDA Agricultural Research Service.
• McGregor, B. M. (1989). Tropical products transport handbook (Agriculture Handbook 668). USDA.
• Sastry, S. K., Baird, C. D., & Buffington, D. E. (1978). Transpiration rates of certain fruits and vegetables. ASHRAE Transactions, 84(1), 237–255.
• Smith, A., & De Cani, P. (1980). An algorithm to optimize the layout of boxes in pallets. Journal of the Operational Research Society, 31(7), 573–578.
• Steudel, H. J. (1979). Generating pallet loading patterns: A special case of the two-dimensional cutting stock problem. Management Science, 25(10), 997–1004.
• Wagner, W., & Pruss, A. (2002). The IAPWS formulation 1995 for the thermodynamic properties of ordinary water substance for general and scientific use. Journal of Physical and Chemical Reference Data, 31(2), 387–535.
• Wagner, W., Riethmann, T., Feistel, R., & Harvey, A. H. (2011). New equations for the sublimation pressure and melting pressure of H₂O ice Ih. Journal of Physical and Chemical Reference Data, 40(4), 043103.