Write the batch process monitoring and improvement chapter - #272
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The planned stub becomes a full page with a single arc: the golden batch and what replaying it can and cannot hold constant (real nylon data: regulated variables repeat to 0.5%, responding variables spread 7.4%); why the outcome still varies, dissected with the bioreactor simulator (replay campaign spread, the variance decomposition into a before-batch share and a during-batch share, and the feed classes in the Z block); predicting a running batch as a missing-data problem (trimmed score regression, with the per-decision-point prediction of one poor batch); and mid-course correction (the Yabuki-MacGregor dead band and validity gate, the Flores-Cerrillo quadratic program with every term translated, per-feed-class local models and why a single global linear model misdirects). Every claimed improvement is executed, not predicted: the corrected schedules are re-simulated with identical disturbances. Headline, forty fresh batches: replay 7.51 +/- 1.20 g/L, corrected 7.71 +/- 0.78 (four corrected, all in the poorest class, +1.53 to +2.67 g/L each, none harmed), against an oracle-from-the-decision-point ceiling of 7.83 and a perfect-feedforward ceiling of 7.82 whose minimum is worse than the corrected policy's. A decision-point sweep locates the correction window mid-batch, and an exploration-dial sweep measures the validity-limit trade-off against the true process. Every number in the prose reproduces from the chapter's own code blocks against process-improve 1.68.0 (verified by running them); make text builds with zero warnings; make html passes with no goatcounter strings. Citation version and date bumped. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
Checked every credited claim against the primary sources. The corrections matter because the people cited are likely readers of this page. - Flores-Cerrillo and MacGregor optimise an adjustment to the latent variable scores and recover the remaining trajectories by inverting the PLS model. The chapter previously described their method as an optimisation over the future manipulated-variable columns, which is what this implementation does, not what they do. Both are now stated, with the trade-off between them. - The SPE penalty on the candidate row, the hard caps, the actuator bounds, the rate limits and the knot parameterisation are additions here, not theirs. Their formulation carries the soft T2 term; SPE appears in their paper as a validity check on the measurements, before any correction. - The SPE validity gate is therefore attributed to the latent variable form of the method, not to Yabuki and MacGregor, whose 1997 formulation predates it. The no-correction dead band remains theirs: it is their no-control region. - Garcia-Munoz, Kourti and MacGregor found conditional mean replacement and trimmed score regression jointly best, giving almost identical predictions, rather than recommending trimmed score regression alone. - Their nylon study identified the controller from 45 batches, 30 with deliberate moves, and reported adequate control from as few as 15 (10 with moves). The chapter said it needed 30, the opposite of the paper's own conclusion about modest data requirements. - Published gains are not almost always predictions: Flores-Cerrillo and MacGregor obtained their nylon final qualities by rerunning the non-linear model with the computed trajectories. It is industrial case studies, where execution is unavailable, that report predictions. - At a decision point the future setpoint columns are not missing; they are set to the schedule under consideration, as in the source paper. Only the future measured trajectories are estimated. - The Z block joined to the unfolded trajectories is credited to Kourti, Nomikos and MacGregor alongside the Nomikos-MacGregor unfolding. - With hard SPE and T2 caps the program is quadratically constrained, not a quadratic program; both forms are now described. - Yabuki and MacGregor's DOI was wrong (10.1021/ie960599o resolves to nothing); corrected to 10.1021/ie960536m. Added the missing DOIs for Flores-Cerrillo and Garcia-Munoz, and moved Golshan et al. out of the methods-used-here list, since LV-MPC addresses setpoint tracking rather than the mid-course correction problem implemented on this page. Also records the review-render rule in CLAUDE.md: these HTML artifacts must not scroll horizontally at any zoom, verified in headless Chromium. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
The author-voice and pedagogy passes of the adversarial review, with two findings checked against the code and the data rather than taken as read. Corrected because they were wrong, not merely infelicitous: - The dead-band explanation at day 2 contradicted the dead band's own definition. The text said uncertain predictions make the band pass more batches, but a wider prediction interval makes the band pass fewer. The real mechanism is that early projections scatter around where batches actually land, so acceptable batches project below target and the same scatter misdirects the correction. Stated that way instead. - The claim that the oracle's schedules reach 5 degC above anything in the training campaigns is false: the training campaigns already reach 39.1 degC against a 39.0 degC actuator ceiling, and the corrector is capped below that at 38.7 degC. What actually puts the best schedule outside the supported region is an unusual combination of setpoints, a warm hold carried past the nominal cooling day, which is what T2 measures. Rewritten to say so, which also explains what T2 is. - The variance-decomposition parenthetical enumerated cases the function does not run. It runs four campaigns: all channels, then each alone. The count was right and the enumeration wrong. - Tag06's spread is quoted to two figures (0.54%) so that the stated ratio to Tag10's 7.38% reproduces as about fourteen times; from the previously displayed 0.5% a reader recomputing would get fifteen. Pedagogy: define "decision point" and "knots" at first use; explain alignment before the first code block uses it; give the monitoring figure the prediction-interval and target context it needs to be read; state the seeding contract that makes the corrected re-run a same-batch counterfactual; say that the campaign wrapper rebuilds the pipeline assembled by hand; name the parameter the decision-day sweep varies; extend the correction code block to draw both panels the figure shows; drop an unused import; name the "mean gain" column's denominator. Voice: positional cross-references replaced with labelled :ref: links; idioms, monetary metaphors, anthropomorphisms and editorial asides replaced with plain statements; three long paragraphs split; units added to the policy table headers and one precision used for the same quantities in the table and the prose. make text: zero warnings. make html: succeeds, no goatcounter hits. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
…ection The chapter read as a demonstration; a reader could not tell whether the method fitted their own process or what the steps were. It now has a section on when mid-course correction is the right tool (four conditions, each with a check a plant can run on its own records, and a table placing the method among monitoring, end-point prediction and feedforward adaptation), and a closing procedure for a plant, including what can and cannot be validated without a simulator and how to deploy in stages with a calibration record. The prediction section now states the three kinds of column at a decision point (with a new schematic), trimmed score regression, the conditioning of the estimator, and the prediction interval at the decision point as an equation, and adds a held-out check of the prediction layer at every decision day. That check exposed that the previous interval, built from the full-row training error, covered 70% of held-out outcomes instead of 95% and was blind to the ill-conditioned early projections of one class; process-improve 1.79 builds the interval at the decision point, and every number on this page is re-measured against it: the funnel now narrows from +/-4.0 g/L at day 0.5 to +/-1.75 at day 4, the dead band asks that the whole interval fall short of the target, five batches are corrected in the campaign comparison (none harmed, sd 1.20 to 0.78 g/L), and the decision-day sweep no longer harms early. Also: the variance decomposition's four shares are stated with their numbers and the interaction share explained; the correction is written as an equation with each term named; the replay campaign is 200 batches and the Z-score plot uses the training campaign, so figures and chapter code agree; and the six dictated wording corrections are applied. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
Fifty-nine findings from practitioner, referee, first-reader, numbers and house-style reviews; the ones that held are applied. The larger additions are what a plant needs and the demonstration had skipped: on-line alignment through a real-time indicator variable; the size and cost of the excitation campaign in engineering units; how to form the feed classes on a plant and the reference-move test for whether local models are needed; which columns hold recorded values and which hold setpoints, and why that matters where a loop saturates; a computable offline consistency check of the model's predicted effect of past schedule moves; a data-only leverage measure by decision day, with its executed counterpart showing what it does and does not capture; bounds as the narrower of actuator and permitted operating range; re-basing golden-batch alarm bands; and a measured sample-size comparison (60, 100 and 200 training batches) showing over-fitting at 60 and half the gain at 100. Accuracy fixes: the interval at day 0.5 does not reach the floor (only day 1.5 does); class A's estimator is still ill-conditioned at day 3 and the day-3 improvement belongs to class C's shrinking error; the day-2 sweep corrects five batches, not fewer; the corrected schedule's descent rate holds only to day 5.5; the full-row error is quoted on the same degrees of freedom as the table; the oracle row is a local search and hence a lower bound on the ceiling; model inversion can carry actuator limits indirectly (Golshan and co-workers); the per-time score covariance is Nomikos and MacGregor's; the package's trimmed score regression is the A-component reconstruction of Arteaga and Ferrer's; Flores-Cerrillo and MacGregor's data-requirement finding is stated as what their data satisfied rather than as a requirement they stated; and the two SPE limits at a decision point are explained. Three cross-references pointed at the wrong labels and are retargeted; every positional reference is now an explicit link; the disturbance-free reference, training mean and class agreement are computed on the page rather than asserted. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
The chapter rework is a substantive change, so the calendar version and release date move to today, as the repository rules require for any pull request beyond a typo fix. Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra
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The planned stub at
product-development-product-improvement/batch-process-monitoring.rst(issue #74) becomes a full page for a mid-to-beginner reader, reworked so that a reader can decide when mid-course correction fits their own process and how to apply it, step by step.Structure
Method change behind the numbers. The held-out check exposed that the previous prediction interval, built from the full-row training error, covered 70% of held-out outcomes at the decision point instead of 95% and could not see that one class's score estimator is ill-conditioned before day 4 (condition number 8e5 at day 2, projections of -146 g/L for a batch that finished at 8.15). kgdunn/process-improve#541 builds the interval at the decision point; every number on this page is re-measured against it: the funnel narrows from +/-4.0 g/L at day 0.5 to +/-1.75 at day 4, the dead band asks that the whole interval fall short of the target, five batches are corrected in the campaign (none harmed; sd 1.198 to 0.782 g/L; 67% of the oracle's mean improvement), and the decision-day sweep no longer harms early.
Review. Six-lens review (practitioner, referee against the four primary sources and the package code, first-time reader, numbers against the run logs, house style, structure): 59 findings, 55 applied, 4 refuted by measurement; the attributions to Yabuki and MacGregor, Flores-Cerrillo and MacGregor, Arteaga and Ferrer, Garcia-Munoz, Kourti and MacGregor, Nomikos and MacGregor, and Golshan and co-workers were each checked against the paper text.
Verified. Every number in the prose reproduces from the chapter's own code blocks run top to bottom against process-improve 1.80 (kgdunn/process-improve#541).
make text: zero warnings.make html: succeeds,grep -r goatcounter _build/html/contentsreturns zero hits. Review render checked for zero horizontal overflow at 375 to 1440 px.CITATION.cffbumped to 2026.09.05.CLAUDE.mdcarries the review-render rule.Companion PRs. Figures: kgdunn/figures#83 (ten PNGs, three scripts; merges first, until then this PR's PDF step fails on the missing images, the known scheduling artifact). Code: kgdunn/process-improve#541 (
MidCourseCorrector.predict, the per-decision-point interval, the dead-band default, a knot bug fix; version 1.80.0).🤖 Generated with Claude Code
https://claude.ai/code/session_01NZAyiPT8xURSdi24yFKCra