Control limits are not specification limits

A run chart tells you whether a pattern is unusual. A control chart adds limits computed from the process itself, which makes the same question sharper and answerable with fewer points.

The limits come from the process. Never from the specification.

This is the single most consequential sentence in SPC, and it is broken constantly.

Control limits describe what the process does. They are computed from its own variation — typically the mean moving range, divided by a constant — and they answer: is this point consistent with the way this process has been behaving?

Specification limits describe what somebody wants. They come from a drawing, a contract, or a customer. They answer a completely different question: is this unit acceptable?

Drawing a specification limit on a control chart destroys both. Points inside the specification but outside control look fine, so real changes go unnoticed — exactly what happened above. Points outside the specification but inside control invite investigation of individual units when the whole process needs changing. And the chart stops being able to distinguish common cause from special cause at all, which is the only thing it was for.

The two questions are both legitimate. Control and conformance are separate, and a process can be in control and unacceptable, or out of control and passing everything.

A variables chart is a pair, and the order of reading is fixed

An X̄ chart's limits are computed from the range chart's centre line. So:

Read the dispersion chart first. If the range or moving-range chart is out of control, the location chart's limits were derived from a spread estimate that does not describe anything. They are not limits; they are arithmetic. Nothing on the location chart can be read until the dispersion chart is settled.

This is why a tool that shows you only the X̄ chart is doing something worse than showing you nothing.

Choosing the chart is the decision

The wrong chart still draws, and it looks entirely normal.

Using an I-MR chart on count data produces limits that can go below zero. Using a p chart on measurements is a category error the arithmetic will not object to.

Rules, and the cost of adding them

Beyond "outside the limits", rule sets look for patterns: runs on one side, points clustered near a limit, trends. Western Electric and Nelson are the two published sets.

More rules means more sensitivity and more false alarms. Each rule has its own false-signal rate on a stable process, and they compound. The usual way to express the cost is the average run length to a false alarm: on rule 1 alone a stable process signals about once every 370 points, and adding the other three Western Electric rules brings that down to about 90 — so the whole set signals roughly four times as often on a process where nothing is wrong. Nelson's eight rules are more sensitive again. Choose a set, state which one, and keep it — swapping rule sets until a chart says what you expected is the control-chart version of choosing your analysis after seeing the data.

The tool opens with the bag weights as an I-MR pair.

1. Read the moving-range chart first — the tool puts it above the individuals chart for that reason, and states whether the limits below it can be trusted.

2. Five signals are listed. Find the rule 4 one at bag 8 and note which points it covers, then switch the rule set to Limits only. Every one of them disappears: no single point is outside the limits. The step change is invisible without the run rules.

3. Switch to Nelson and compare. It flags the same five moments — a published set does not invent different history — but under different rule numbers, and its first signal arrives at bag 9 rather than bag 8 because Nelson's run rule needs nine points where Western Electric's needs eight. That one-bag difference is the whole practical gap here. The sets genuinely do differ; on this data they happen to agree, which is worth seeing too, because it is the reason the choice has to be made before the data rather than after.

4. Delete bags 15 to 24 from the box. With only the first fourteen, the limits recompute around the original level and there is no signal at all: the chart was never detecting a bad process, it was detecting a change.

5. Switch the rule set back to Western Electric — step 3 left it on Nelson, and the rest of this step is about which Western Electric rules survive. Now change the chart type to c (count of defects). The tool swaps in a c-chart sample, so paste the bag weights back in over it. They are whole numbers, so the chart draws without complaint — and its limits come out at about 438 to 573, because a c chart assumes the variance equals the mean and estimates the spread from the centre line alone. Against a process whose real limits are 493 to 518, that is a sigma of 22.5 where the truth is 4.1.

   Read what survives and what does not. No point can ever fall outside those limits — the whole specification sits comfortably inside them, so rule 1 is dead. But rule 4 still fires at bags 8 and 22, because "eight points on one side of the centre line" counts points against the centre line and does not care what sigma is. The zone rules that DO depend on sigma — 2 and 3, which found the step change on the I chart — go silent, because all twenty-four bags now sit inside one inflated standard deviation.

   So the wrong chart does not fail loudly. It keeps the one rule that happens not to need the parameter it got wrong, loses the two that do, and looks entirely ordinary while doing it. That is the failure mode the chart-type decision exists to prevent.