0041 — A characteristic the plant counts, and the chart that judges it

• Status: accepted (2026-10-11, by the maintainer)
• Date: 2026-10-11
• Deciders: maintainer
• Amends: 0040

Context

0040 made the chart type a property of the data: the sampling plan is on the specification and the chart follows from it, individuals one piece at a time and X̄/R when the plan says n at a time. Both of those charts plot a measurement. Something was measured; there is a number; the limits come from how much that number scatters.

A great deal of what a plant knows about its own quality is not a measurement. Somebody looks at every bottle that reaches the inspection station and sends some of them back. What that produces is two whole numbers for a stretch of production — how many were looked at, how many went back — and, if the plant codes its rejects, which defects they were. There is no reading, no gauge, no spread. Before today this product had nowhere to put that, which meant the commonest quality record in a bottling plant, a packaging plant or an assembly line could not be written down at all.

The temptation is to write a quality_checks row per unit with a pass or a fail on it. 0027 refused that and the refusal stands: a check is a reading of a characteristic, with a stamp, a gauge and a value, and twelve hundred rows carrying "pass" are twelve hundred rows that are not readings and that every chart, every capability figure and every coverage sentence in the product would then have to learn to ignore. What the plant actually recorded is one record about one stretch.

The other temptation is a "chart type" field beside the sample size. 0040 refused that too, for the reason that has not changed: two fields that can disagree, and the disagreement is a chart that lies.

Options considered

Option	For	Against
The specification says it is counted; one new table holds N, k and the defects; the chart follows as a p chart	One fact decides the chart, as in 0040. The record is the record the plant made — a stretch, two numbers, a breakdown — and nothing has to be inferred from it. The write, the rules, the holds and the dossier are the paths that already exist	A third kind for everything that reads kind to learn, and a third branch in the page, the kit, the agent's reader and the simulator's scorer
A quality_checks row per unit, with pass or fail in the value	No new table. The existing chart machinery sees "data"	Refused by 0027 and still wrong. A pass is not a reading; the rows are not what anybody recorded; and every figure computed from quality_checks would quietly include them
A chart-type field on the specification, chosen by hand	A plant could draw what it liked	0040's argument, unchanged: two fields that can disagree. And a counted characteristic has nothing for the other two charts to plot, so the disagreement is not a preference, it is a blank chart
np, c and u charts as well, now	Completeness. A plant with a fixed inspection quantity reads np more naturally	Three more kinds, three more sets of limits and three more things to explain, for a chart that is p's own numbers times a constant. A plant that needs them can say so; this is the one that fits what a plant records without being asked
Per-point limits, or one pair from the pooled average n	A single pair of straight lines is easier to read, and is what most textbooks draw	A stretch of two hundred and a stretch of two thousand are not judged to the same standard, and straight lines would say they were. The honest chart has a pair per point

Decision

A characteristic whose specification says counted is counted, not measured. Its record is one row per inspected stretch in quality_counts — how many were looked at, how many were sent back, which defects, and what the plant calls the lot — and its chart is a p chart whose control limits are computed per point.

QualitySpec.counted is the third word in the one place the chart type is decided (services.spc.chart_kind). counted wins over sample_size, because a counted characteristic has no readings for the other two charts to plot; the write path refuses a specification that claims both, and fsmes pack check refuses one offline, with its own sentence.

POST /quality/counts is the write, under quality.record like every other quality write, and is the mirror of POST /quality/samples: one row, however many units it covers. It takes inspected, rejected, a lot_ref in the plant's own text, an optional breakdown of [{code, count}], the order, the station, the stretch's start and end, and an optional lot_id into material_lots for a plant that ships lots. lot_ref is required and lot_id is not: on a plant that does not ship lots yet the honest answer is what the plant calls the stretch, and the screen says so under every lot it opens — a lot here is one inspection stretch on one order until this plant ships lots. Nothing is backfilled. A characteristic that is measured refuses this write with a sentence naming the chart it does have.

The chart plots p = k/n per stretch. The centre is pooled — Σk/Σn, not the mean of the shares — because a stretch of two thousand says more about where the process sits than a stretch of two hundred, and averaging the shares would weight them equally. Each point's limits are p̄ ± 3·√(p̄(1−p̄)/nᵢ) with its own nᵢ, so the pair moves with the lot; they are drawn as steps, held flat across half the gap to each neighbour, because nothing moves between two lots and a sloped line would read as a limit that drifts. A lower limit that computes below nought is drawn at nought and the chart says what that means: too few units were looked at for a clean lot to be remarkable, so nothing on that lot could fire a rule downward.

Rule 1 only. A point outside its own limits is the signal, recorded and held through evaluate() on the write path exactly as on the other two charts (0027, 0036). Rules 2, 3 and 4 count points inside sigma bands, and on a p chart every point's sigma is a different width — two points "beyond two sigma" would be two points measured against two different rulers, and a run of them would be a pattern in the inspection quantities as much as in the process. Rule 5 is a range beyond its limit and there is no range here. The chart draws the rules it runs and says in words which it is not running and why, rather than leaving a reader to notice that a run of eight did nothing.

No capability. Cp, Cpk, Pp and Ppk are a spread against a specification and a count has neither: there is nothing to be in or out of spec about on one unit, and what judges a stretch is the control limits of its own chart. The three cells say "not for a count" and carry that sentence; no figure is printed, and none is withheld silently.

The point dossier opens on a lot (GET /quality/spc/{material}/{characteristic}/lot/{count_id}) and its first block is which defects, because the dot says more of this lot came back than usual and the only useful next question is which ones. Its window is the stretch, not the instant the count was written down. Below the first three blocks it is the same dossier a reading and a sample open — the machine, its Gantt, the rest of the line, the process values, the maintenance, the findings — read from the same keys, so there is one panel and not a third one that would drift.

Three different facts about a breakdown, three different sentences. A null defects is this MES does not know how they were sorted; an empty list is nothing was coded against the rejects; a coded total that differs from rejected is a unit carrying two defects, or an inspector who coded some and not all. The screen prints which, and never draws a clean lot for any of them.

Consequences

Easier: the commonest quality record on a packaging or assembly line can be written down, charted, and argued with, from the same write path, the same rules, the same holds and the same dossier as a measurement. A plant that counts rejects per lot gets the chart that judges those counts honestly instead of a spreadsheet.

Harder: kind now has three words, and everything that reads it had to learn the third — the page, the chart kit, the agent's chart reader, the simulated plant's chain scorer. Each of them now names a kind it does not know and says so, rather than drawing a share as if it were a millimetre. That is the cost of the decision in 0040 that the chart type is a property of the data, and it is paid once per reader.

Harder: a reader who knows X̄/R has to be told that the limits on this chart are not straight. The chart tells them, in its footer, every time.

Not decided here, and named so nobody builds them by accident:

• np, c and u charts. A plant whose inspection quantity never changes can read np, and a plant counting defects rather than rejected units needs c or u. Both are the same records with different arithmetic on them. When a plant asks, the table is already right.
• Scrap reason codes. The defects on a count are the plant's own words and this product does not police the vocabulary. A managed list of reason codes, with a hierarchy and a Pareto that rolls up, is a separate piece of master data: docs/design/backlog/scrap-reason-codes.md.
• Finished-goods lots. lot_id is there for a plant that ships them. Making this plant ship them is not this decision.

House rules touched

Never invent production (1): a stretch in which nothing went through the inspection station posts nothing, rather than a lot with nought looked at — a point at nought rejects for a quarter of an hour when the machine was down is a chart saying the plant was perfect while it was stopped. A counter that goes backwards re-baselines and books nothing. inspected and rejected are the record; the share is arithmetic on them and is never stored.

Unknown is not zero (2): a null breakdown is not a clean lot, and the screen says which of the three facts it is holding. A lower limit at nought is a sentence, not a line nobody explained.

Every list states its total (3): the defect table states how many codes, how many units were sent back, and how many of them were coded — three totals, because they can honestly differ.

Config, not code, at plant boundaries (4): counted is in the pack's quality_specs.json and on the Specifications tab; fsmes pack check refuses a counted characteristic that also asks for samples, or that carries specification limits, offline. Which defects a plant sorts rejects into, and what it calls a stretch, are the pack's.

Tests are named as prose (5): the suite for this reads test_a_characteristic_the_plant_counts.py.