Three batch case studies for the Applications chapter (DuPont batch PCA, SBR batch PLS, FMC multiblock batch PLS)

[kgdunn]

Three worked case studies on batch data for the Applications chapter, placed after the batch process monitoring page. They are the book-side counterpart of the three case studies added to process-improve in kgdunn/process-improve#537 (issues #154, #155 and #156 there, merged), and every figure is generated by a matplotlib script in kgdunn/figures#84, #91 and #92.

The three pages are read as three separate HTML pages and as consecutive pages of the PDF, so each one says where it sits in the set: every introduction names what the earlier pages contributed, the SBR page points forward to the FMC blocks where the attribute it predicts last is set, the DuPont and FMC pages point at the SBR on-line section for the sample-by-sample check, and each closing paragraph hands over to the next page.

This PR is paired with the 1.83.2 release, which is now on PyPI. The three batch pages import loaders and on-line methods that no earlier release carried, and the FMC page's cell-wise cross-validated value needs the 1.83.1 fix that lets the element-wise scheme cross-validate a block which already has missing cells.

What changed

• product-development-product-improvement/batch-case-study-dupont.rst (label APPS_batch_case_dupont): batch PCA on the 55 batches of the DuPont polymerization reactor. Model A on all batches, the SPE outlier (batch 49) diagnosed with SPE contributions per tag and per sample (the event Nomikos, 1996, attributes to the heating system), the score outliers (batches 50 to 55), the second group found after rebuilding (batches 37, 39, 43 to 48) read as a cluster against the model centre (a contribution runs between two points, and either can be an actual observation or a synthetic one: the model centre, or a group average the reader supplies; the model B score plot draws that direction as an arrow from a square at the group's average point to the centre, and the contribution figure pairs the per-tag bars, each member a dot, with the raw trajectories of the three largest-contributing tags and Flow-2 over the first 30 samples), and the final model C on the remaining 40 batches, verified by projecting the 15 left-out batches onto it: all 15 lie above its SPE limit, seven above its T2 limit as well, while the four poor-quality batches kept in the training set (38, 40, 41, 42) stay inside both limits, the observability lesson. The page says that the original study also left those four out and built its monitoring model on 36 batches with three components, and it compares the two unfolding layouts as Westerhuis, Kourti and MacGregor (1999) measured them on this same data set. The quality list from the laboratory records plays no part in building any model.
• One meaning per colour on that page, after review: the second group is purple triangles in every figure it appears in (it had been orange in two figures and purple in a third, where orange already meant batch 49), and the four poor-quality batches are magenta diamonds in the model C figure, whose two panels sit side by side. Shape carries the identity alongside colour, so each set is recognised across figures and in print. The choice was checked with a colour-vision and contrast validator against the four colours each shares its figure with. The code blocks now draw those highlights themselves, rather than leaving them to the committed figure while the caption described them.
• product-development-product-improvement/batch-case-study-sbr.rst (label APPS_batch_case_sbr): batch PLS from six trajectories of the simulated SBR reactor to five latex quality attributes. The faults are stated as Nomikos and MacGregor (1994) simulated them: 30% more impurity from the start of batch 37, 50% more from midway through batch 34. The two batches land in different places of the score plot, whose marker area carries each batch's SPE, so the plot answers both questions asked of a batch; contributions, time-varying weights, per-cell R2, a sustained-departure diagnostic on the raw trajectories (a signed distance from the other batches in their standard deviations, and a robust version from the median and 1.4826 MAD smoothed with an EWMA, drawn together as dashed and solid lines), and the fitted quality of the faulty batches against their measured values, with RMSEE and the leave-one-batch-out RMSEP printed on the panels and a band of two RMSEP around the parity line. Two further sections answer the page's third question, whether the model could have said so while the batches were running: "Predicting quality before the batch ends" (label APPS_batch_case_sbr_online_prediction) traces the final-quality prediction from a batch-so-far with the library's missing-data score estimate, as the leave-one-batch-out RMSEP per attribute (with the sample at which each attribute's error falls below its standard deviation, the error averaged over the five attributes, and the reason the particle size is predicted last, from the 1995 paper) and as batch 4's evolving prediction against its final prediction and measured value; "Would the model have caught it on-line?" (label APPS_batch_case_sbr_online) fits a reference model on the 51 normal batches, explains why the T2 limit is the same at every sample while the spread of the score estimates is not (with a figure of that spread falling over the batch, and the per-sample covariance credited as the 1995 paper states it and the 2004 paper computes it), runs batches 37 and 34 through per-sample T2 and SPE limits (compared with the samples at which the original papers flagged the same two batches), reads the residual shares at the alarm sample, lays out as a chain of bullets the false-alarm rate of the three-sample rule on the reference batches (the autocorrelated single-sample SPE flags one normal batch in four, a smoother limit through spe_window does not change that, the cumulative SPE does at the price of a later detection, and the 99.9% residual limit of Nomikos, 1996, does without one, with the wider point made by Ramaker et al., 2006), and shows the trajectory forecast of Wold et al. (2009) for both faults.
• product-development-product-improvement/batch-case-study-fmc.rst (label APPS_batch_case_fmc): the ladder of two-component models on the FMC batch dryer, introduced as a bulleted ladder (PCA on quality, PLS from each initial-condition block, multiblock PLS on both, batch PCA and batch PLS on the trajectories, batch multiblock PLS on all three blocks), with the clock time at each aligned sample as the eleventh trajectory of every batch model, as in the original study, and the operating-condition block described for what it is: the cake weight and eight landmarks read off the trajectories at the alignment. The data section is half its earlier length, in short paragraphs. Every score plot on the page is coded by the plant's classification, a colour and a marker shape per class (blue circles good, purple triangles abnormal, gold squares high solvent), through a group_scatter helper in Plotly, and the bar charts shade alternate positions behind the bars. The multiblock PLS on the two initial-condition blocks is drawn as a 2 x 3 figure: the super scores in the first column, and for each block its scores above its weights, so that batch 20, inside the chemistry cloud and far outside the operating-condition one, is read against the weights that place it there. The loading panels of the batch PCA carry the cumulative R2 of every cell after two components on a second axis, and the two phase ends are marked on the raw overlays, the loading panels, the per-sample panel of batch 20's contribution figure and the raw panels of the four-batch figure. Batch 20's SPE contributions, computed by the library from its observed cells, replace the batch-41 figure and the paragraph that said contribution plots need complete trajectories. A table near the end gives the R2 of each block, per component, for every model of the ladder, and the on-line paragraph says that every method on the page handles a batch observed so far and points at the SBR section that shows it. A section (label APPS_batch_case_fmc_block_scores) reads the block scores of the final model: four batches classed good (2, 3, 6, 7) sit among the abnormal batches in the trajectory block and among the good ones in both initial-condition blocks, and what separates them from their nearest abnormal neighbours is the length of the later phases (a longer cool-down, a shorter and steeper ramp), not a set point that was moved; its closing bullets say what the record can and cannot tell about why, with the caution of Nomikos and MacGregor (1995) that the model describes correlation, not cause and effect.
• Later rounds on the FMC page, from review: a three-panel figure of what the alignment did (the dryer temperature against clock time, the same batches against aligned sample, and the clock time at each aligned sample, with the shortest, a middling and the longest batch drawn in colour, and the echoed numbers behind the sentence: 59 batches, 93 to 200 time units, every one aligned to 325 samples); a figure for the operating-condition PLS, so the passage on batch 20's recipe timings has something to look at rather than three numbers quoted in the prose; batches 61 and 14 named in every later score plot, so the two quality groups can be followed from figure to figure; the three phases named on the per-sample panel of batch 20's contribution figure, each at whichever end of its phase the bars leave headroom; and "disposition" replaced by "classification" on this page and the one sentence that used it on the DuPont page.
• A later round on the quality ladder, from review: the multiblock PLS on the two initial-condition blocks now has its own row in the ladder tables, so the reader meets its 29.2 and 36.4% in a table rather than only in prose. The tables accumulate one rung per section: three rows after the two single-block PLS models, four after the multiblock section, five once the trajectory block is added. Neither the multiblock nor the batch PLS row carries a cross-validated value, and the caption now gives both reasons. Three prose fixes went with it: the dryer temperature tag is named in monospace where its loading changes sign, the missing-cell paragraph drops a walk-through of batch 20's scores and keeps the point, and the explanation of the empty Q2 cells is corrected. It had said a PCA has no second block to predict a held-out batch from, which contradicts the cross-validation section of the latent-variable chapter; a PCA can be cross-validated by rows, and the objection is that the held-out row supplies the scores that rebuild it, so the value reaches 100% once the components equal the variables.
• The first row of the quality ladder now carries a cross-validated number. It had none, because the element-wise scheme could not cross-validate a block that already has missing cells, and the dryer's quality block has 19 of them; that is fixed in 1.83.1. The page holds out a seventh of the measured cells at a time and averages over fifty groupings, giving 33.4% after one component and 25.1% after two. One grouping is not steady enough to print: the second-component value swings 13.9 to 33.4 across ten seeds, where fifty leave a seed-to-seed spread of about a point. The value sits in the shared Q2 column, beside a new held out column that says what a held-out group is in each row: single cells for that PCA, whole batches for the two PLS models. That column is what makes one shared column legitimate, because the PCA row answers a different question from the two PLS rows: how well one attribute is predicted from the other seven of the same batch, not how well all eight are predicted for an unseen batch. The paragraph that used to explain the empty cells shrank accordingly, and the two PLS rows are still comparable with each other and with every later rung.
• A new FMC section, "How many components does the quality block support?", tables the fit and the cell-wise cross-validated value over four components, since the chapter fitted two and printed the value in passing without ever saying what it was for. The two part company at once: R2 climbs 50.0, 70.3, 78.8, 86.6% while Q2 goes 33.4, 25.1, -44.6, -84.2%, so a three-component model predicts a held-out cell worse than the block's own average. The two-component model is kept and the section says why: the second component is what separates the classes in the score plot, and every model in the ladder is read at two components, which is what makes the rungs comparable. The cross-validation moved up to where the model is fitted, so the chapter computes it once. No number already in the tables changed; the two that were there are the first two of the four now shown.
• The prose was shortened and rebuilt to the style guide, after review. The pages read as walls of text: paragraphs of 100 to 190 words, and one 536-word bullet block on the SBR page. Two passes fixed it. The first split, cut or bulleted every paragraph over 90 words. The second applied "keep the claim, its reason and its consequence, and stop" sentence by sentence, and removed the colons and semicolons splicing two ideas into one sentence, which CLAUDE.md forbids and which the first pass had introduced. Lists that were running prose became bullets: the dryer's three phases, the two readings of a PLS weight, the two ways of summing a contribution, the two statistics that catch batches 34 and 37, the three responses to the SPE false-alarm rate. Prose across the three pages fell from 10,228 words to 8,424; the DuPont page, the one reviewed, is down 29% with a median paragraph of 42 words and none over 70. No detail was dropped: every number, citation, cross-reference and defined symbol is kept, and no code block was touched.
• Labels on the score plots are placed by measurement, not by hand. In the chapter's Plotly code a label_corner helper puts each batch's name in the emptiest quarter around its marker, in units of each axis's own range so the choice matches what the reader sees, and counts each name it places as a neighbour for the next, so two batches side by side take different corners. Checked for every labelled batch on the four score plots of the page: each lands in a corner with no neighbour within a tenth of the plot. The committed PNGs get the equivalent treatment in DuPont figures: the eight-batch cluster keeps one colour and one shape figures#92, where a checker reports any label that runs off the figure, intrudes into a marker, lands on another label or sits under a legend.
• Every score plot on the three pages carries the percent of variance each component explains on its axes (R2 of X per component, labelled R2X on the PLS-type models and their block scores; R2Y on the multiblock super scores), and the prose no longer repeats numbers that can be read off a plot. Hotelling's statistic is set as maths throughout the prose, including in the three places where it sat inside :ref: link text and a maths role cannot nest.
• The references on the three pages link to literature.learnche.org where an entry exists (thirteen papers and chapters), and four names on the pages link to their source in the process-improve repository (batch_dtw, BatchPCA, BatchPLS, MBPLS).
• product-development-product-improvement/batch-process-monitoring.rst: a short paragraph pointing at the three case studies, three further readings added to the list (Westerhuis, Kourti and MacGregor, 1999; Garcia-Munoz, Kourti and MacGregor, 2004; Arteaga and Ferrer, 2002), a subsection on the scores of a batch observed so far, which names the three missing-data estimators the library offers and why a projection is preferred to filling the future with an average trajectory, and the reading list renamed to "References" with a label (APPS_batch_readings) so the case studies can send the reader to it.
• .github/workflows/check-code.yml: the pyoptex chapter job installs process-improve[expt,batch] rather than [expt]. That job runs the whole product-development chapter so the mixed-level page sees the namespace its chapter builds, and the chapter now also holds two pages that read an openmv.net workbook, whose Excel reader lives in the [batch] extra. Neither extra pins plotly, so the pair still resolves against pyoptex's plotly 5.
• Makefile: check-code-chapter and check-code-file pass --strict-output, as check-code already did. Without it a per-chapter run reported a number that had stopped reproducing but still passed, so a quick local check proved less than it appeared to.
• CLAUDE.md: the writing and figure rules distilled from the review of these pages (length and focus, paragraph construction, figures and captions, process), added under the author's voice section so the same corrections are not needed again.
• product-development-product-improvement/index.rst: the three pages in the toctree after batch-process-monitoring.
• latent-variable-modelling/principal-component-analysis/latent-variable-contribution-plots.rst: a label (LVM_contribution_plots) so the case studies can cross-reference the contribution-plot section.
• CITATION.cff: version 2026.09.10, date-released 2026-09-10.

The LDPE cross-validation page is no longer part of this PR. This branch had refreshed its Q2 numbers after process-improve #546 changed how the element-fold scheme judges convergence; #287 has since landed the better version of the same fix on main, passing the raw block so that no warning is raised at all, and this branch now carries main's file unchanged.

Every figure has a Plotly code block before it, following the chapter rework playbook; each page reads top to bottom as one script. The data come from openmv.net (polymerization.csv, batch-dryer.xlsx, sbr-batch-reactor.xlsx, all three live) through the load_dupont, load_fmc and load_sbr loaders of process-improve 1.83.2, whose BatchPLS.predict_online, predict_online_trace, online_rmse and BatchMonitor the two on-line sections use. The FMC page also depends on two changes in #537: contributions for rows with missing cells (batch 20's figure) and the fix to PCA.r2_per_variable_ on the NIPALS path (the R2 curves of the loading panels; the collector-tank cells read 0.07 before the fix and 0.78 after).

Verification

• tools/check_code_blocks.py (the gate from Execute every Python case in the book in CI, and fix the drift against process-improve 1.78 #274) on each of the three pages with --strict-output, which compares the results echoed in the code, against the released library, every data set read from openmv.net: DuPont 9 blocks, SBR 15 blocks, FMC 14 blocks, all passed. Run as a chapter up to the FMC page: 71 blocks, all passed. Every number the FMC prose quotes is echoed after the print that produces it.
• The whole product-development chapter under the pyoptex job's environment (process-improve[expt,batch] plus pyoptex, which resolves to plotly 5.24.1): 101 blocks, all passed, 0 skipped, 11 minutes, well inside the job's 45-minute timeout. That rehearsal is what the workflow change above is based on, and the job itself is green on the current head against the release.
• Every number quoted in the prose reproduces: DuPont R2 55.9% cumulative for model A, batch 49 SPE 39.3 against 29.1 with 80% of its SPE in samples 55 to 65, the group's mean t2 and t3 of 15.0 and 14.8 against -3.0 with 66% and 90% of the contribution in samples 0 to 25, the 15 left-out batches all above model C's SPE limit and seven above its T2 limit, batches 38, 40, 41, 42 inside both; SBR R2Y 65.3 / 6.9%, the per-fifth contribution shares, the sustained-departure samples (37: conversion 9, latex density 13; 34: temperatures and energy released 103 to 105, conversion 123, latex density 129; the robust version within a few samples of these), the SPE ranks of the two faulty batches (37 the smallest of 53, 34 the twelfth), and the RMSEE and leave-one-batch-out RMSEP of the composition (0.00106 and 0.00122) and the particle size (1.87 and 2.42); SBR on-line: leave-one-batch-out RMSEP / sd averaged over the five attributes 2.99, 1.39, 1.06, 0.62, 0.58 after 10, 25, 50, 150, 200 samples, first sample with the error below the sd 48 (composition), 129 (particle size), 50 (branching, cross-linking), 21 (polydispersity), batch 4 predicted at 1251 after 10 samples against 1257.1 final and 1256.9 measured, T2 limit 10.5, batch 37 T2 alarm after 23 samples, batch 34 SPE alarm after 105 samples (five after the impurity enters), reference false-alarm rates 0.2% and 1.2% with three-sample SPE alarms in 13 of 51 reference batches (one for T2), pooled limits 1.34% and 15 of 51 with batch 34 still at 105, cumulative SPE 3 of 51 with batch 34 at 112, the 99.9% limit 0 of 51 with batch 34 at 106, residual shares 40 / 30 / 16 / 11% at the alarm sample; FMC quality block R2 50.0, 70.3, 78.8, 86.6% and cell-wise Q2 33.4, 25.1, -44.6, -84.2% over four components, the R2 ladder 70.3% (PCA on Y), 22.2 / 26.2% (PLS per Z block), 36.4% (MBPLS on Z), 37.6% (batch PCA), 41.0% (batch PLS), 47.0% (batch MBPLS) with super VIP 0.86 / 1.07 / 1.06, the per-block, per-component R2 of every model in the comparison table, the phase ends at samples 175 and 249, the 59 batches running 93 to 200 time units before alignment and 325 samples after it, the R2 per cell averaged per tag (collector tank level and clock time 0.71, agitator speed 0.08), batch 20's SPE contributions (205 missing cells between samples 34 and 109; dryer pressure 49%; 58% of the total in the first phase, where its dryer pressure averaged 85 units against 37 for the average batch), batch 13's leading contributions from the clock time and the collector level, batches 2, 3, 6, 7 placed with the abnormal batches by the trajectory block and with the good ones by both initial-condition blocks, their nearest abnormal neighbours 42, 43, 44, 47, 50, the four's ramp 24 against 32 clock samples and cool-down 50 against 38, peak set points 86.9 against 87.2.
• make text: zero warnings, after the prose rewrite, after the merge of main, and after the component-count section.
• make html: builds, with no goatcounter string anywhere in the output.
• No em-dashes in the added prose; no prose line longer than 100 characters in the three new pages.

Related pull requests

• Figures: Figures for the DuPont, SBR and FMC batch case-study pages figures#84, §7.3: add 5 PNG figures, fix nested-loop indentation, nuance the re-fitting note #91, §7.3: subgroup the multivariate analysis, add twin-axis comparison, recolour loadings #92 and §7.3: redefine phases (drop unsettled 15-Dec), use score_contributions #93, all merged. §7.3: subgroup the multivariate analysis, add twin-axis comparison, recolour loadings #92 carries the DuPont colour and marker consistency, the FMC alignment and operating-condition figures this PR adds, and the measured label placement with the checker that verifies it.
• Library: Batch case studies: DuPont batch PCA, SBR batch PLS, FMC multiblock batch PLS (#154, #155, #156) process-improve#537 (merged), the loaders, the on-line methods and the missing-cell contributions these pages use, score_plot: let the marker area carry a value (sizes=) process-improve#549 (merged), score_plot(sizes=...), and MBPLS: pool the super score of a row that has missing cells, and score a row missing a whole block process-improve#551 (merged), which pools the super score of a multiblock row that has missing cells. All three ship in the 1.83.0 release, and the tree they sit on is now published as 1.83.2, which this PR is paired with. #551 moves the FMC numbers slightly, since ten of the 46 batches have missing trajectory samples: the combined model explains 47.0% of the quality block rather than 47.2%, and six other numbers on that page move in the third decimal. The page was updated for them.
• Still open: Three more ways to choose a PCA component count, and retire the fourth process-improve#554 adds three more cross-validation schemes to PCA.select_n_components and deprecates the row-wise one. Nothing on this branch depends on it. The FMC quality block is the dataset that exposed a defect it fixes, and a Simca-P column for the new component-count table is expected once those values are to hand.

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[kgdunn]

A final check before review

A last pass over the three pages against the data sets, the library, and the papers they cite, with every quoted number recomputed against the released 1.83.0 on the live data. Nine lenses (statistics, papers, numbers, expert reader, style, cross-page consistency, figures, code, RST), each finding then put to an adversarial verifier that read the source before ruling. Twelve findings were refuted, one of which would have replaced a correct sentence about the SPE with a false one.

The gate was letting numbers through

tools/check_code_blocks.py compares an echo comment with what the block printed, but only when the comment does not "read as prose", and that test counted every word including the quoted keys of a dict. A printed dict of tag names therefore looked like a sentence and was dropped. The DuPont page had no echo the checker kept at all, and all five on the SBR page were discarded, so the numbers those pages quote in print rested on nothing the gate could re-check.

Words inside quotes no longer count, and three numbers or more mark a line as a result. Sixteen comments across the book become checked, every one an echo of real output; no genuine explanation was caught up in it. Echoes were then added after every print on the DuPont page and the four on the FMC page that had none.

That change caught a wrong number immediately, and so did CI on run 90: the FMC page said seven batches classed high in residual solvent were fitted low by 0.58 in a span of 1.41. There are six, fitted low by 0.47 in a span of 1.26, and the page said "six" ten lines earlier.

Corrected against the data

• Batch 20's other-batch dryer-temperature average is 23.7, not 23.6.
• Batch 13 did not collect the least solvent, reach that level in the fewest clock samples, or cool fastest: it is 11th from the bottom on the collector level, 4th on the clock time at the end of the first phase, and its cooling phase is the fifth longest of the 46.
• Five batches classed good sit among the abnormal in the trajectory block, not four.
• Batch 13 is not furthest along the first component; batch 10 is.
• Y11 is not mirrored between batches 61 and 14: it is batch 61's largest contribution and batch 14's smallest.
• Batch 20 ran hot in solvent collection, not over the ramp; over the ramp it is the dryer pressure that stays high, on 89% of its observed samples there.
• Temp1 and Temp2 are the dryer temperature at the end of the first phase and the peak, not initial temperatures.
• The operating-condition block holds no length of the first phase: Time1 equals Time2 plus Time3 exactly for every batch, so it records the ramp and the cool-down only.
• "24 clock samples" is clock time, not aligned samples: in the aligned record the ramp is 74 samples for every batch.
• The dryer-temperature loading changes sign at about sample 130, not at the phase end at 175.
• Batch 53, not 55, has the highest t2 in DuPont model A, and was never read although the section names five score outliers. Batch 51 is not far out along the components, which the page says itself two pages earlier.
• Batch 49's cooling-medium temperature dips from sample 56 and rejoins by 65, rather than falling away after 60.
• On the second component of the DuPont group, TempC-1 and Press-3 carry 46% of the displacement, and Press-2 is as large as Press-3.
• The departure analysis records no onset for batch 34's reactor temperature: it leaves the band but its longest run outside is 11 samples against the 20 the rule needs, so it did not find the reactor-then-service order the residual shares show.

Corrected about a method

A squared residual over the sum of squares is a share of the squared SPE. The reference batches' alarm rate is a lower bound, since the limits were fitted to those batches. The parity band is two leave-one-out errors, wider than the scatter of the fitted values inside it. Only one of the two initial-condition blocks is measured before the batch runs. The chemistry block's 52% is cumulative over two components while its 6.5% is one component of another model. The reactor temperature's weights change sign from sample to sample rather than barely moving. The sample reported for an alarm is the first of the three consecutive ones, so an operator sees it two samples later.

Corrected about a paper

Wold and co-workers build thirteen landmark features on this dryer, each read from one phase, not blocks grouped by what they describe; their chapter sets out the projection to the model plane and points elsewhere for the other estimators, so trimmed score regression is no longer attributed to its equations. The second DuPont group is the group Nomikos and MacGregor single out in the same plane of a three-component model of the same 48 batches, and is now credited to them. The variable-wise summary of the residual is not due to the 2003 paper. The original dryer study is a troubleshooting analysis of historical data and builds no monitoring tools. Comprehensive Chemometrics 2.10 is the chapter and 2 the volume. Three citations of "Nomikos and MacGregor (1995)" now name the paper, since the reading list carries two from that year.

Figures made to show what the captions send the reader to look for

The chapter's own Plotly code did not draw the spokes and group-average crosses the block-scores caption describes, drew the DuPont model A plot in one colour where its caption names two, coloured two batches in the alignment figure where the caption and the PNG show three, paired the wrong quantities in the multiblock middle panel, drew the per-cell panel where the caption promised two, left batch 47 unlabelled though the prose names it, and titled a bar chart "after 105 samples" while plotting the shares left in the variable by the last turn of a loop. In the committed figures the group-average crosses sat under the markers that hid them, the contribution arrow pointed against the contribution it labels, and the bar-chart legend sat on the two tallest super-VIP bars (kgdunn/figures#95).

Verification

• make check-code over the whole book with the stricter echo rule: 7 chapters, all passed.
• make check-code-chapter CHAPTER=product-development-product-improvement: 102 blocks, 77 passed, 25 skipped for pyoptex, 0 failed.
• make text: zero warnings. No prose line over 100 characters on the three pages.
• check_labels.py on all three figure scripts: clean.
• Regenerating all 36 case-study PNGs reproduces the committed files pixel for pixel apart from the three this pass changed.
• The branch was conflicting with main on CITATION.cff, which is why no workflow had dispatched since 22:48; the merge is in and the date kept at today's.

Companion changes: kgdunn/figures#95 (three figures) and kgdunn/process-improve#553 (the SBR page's batch 4 is nearest the average quality, not trajectory, and two stale printed results on the FMC page).

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