Did something actually change, or is this how the process always behaves?

Build an I-MR, X-bar R, X-bar s, p, np, c or u chart with Western Electric or Nelson rules, and read the dispersion chart first — because the other chart's limits come from it.

Control Chart · control · Yellow Belt · free, no account needed

Use this when

You need to know whether a shift in a metric is real before acting on it
You are setting up ongoing monitoring rather than a one-off analysis
Everything is inside specification and problems keep reaching the customer

Control Chart

sandbox

The dispersion chart is in control, so the limits on the chart below it were derived from a variation estimate that means something.

Moving range chart. Dashed: centre line. Solid: control limits (3σ, MRbar / d2(2), d2(2) = 1.128). Squares mark points beyond the limits or involved in a rule violation.

Show the data behind this chart

Moving range chart: 23 points, centre line 4.65, upper limit 15.2, lower limit 0. No points beyond the limits and no rule violations.
#	weight	UCL	Beyond limits
1	4	15.2	no
2	7	15.2	no
3	5	15.2	no
4	3	15.2	no
5	6	15.2	no
6	4	15.2	no
7	3	15.2	no
8	5	15.2	no
9	3	15.2	no
10	2	15.2	no
11	4	15.2	no
12	7	15.2	no
13	2	15.2	no
14	12	15.2	no
15	4	15.2	no
16	7	15.2	no
17	5	15.2	no
18	3	15.2	no
19	6	15.2	no
20	4	15.2	no
21	3	15.2	no
22	5	15.2	no
23	3	15.2	no

Individuals chart. Dashed: centre line. Solid: control limits (3σ, MRbar / d2(2) = MRbar / 1.128). Squares mark points beyond the limits or involved in a rule violation.

Show the data behind this chart

Individuals chart: 24 points, centre line 505.5, upper limit 517.87, lower limit 493.13. 5 rule violations involving 24 points.
#	weight	LCL	UCL	Beyond limits
1	502	493.13	517.87	no
2	498	493.13	517.87	no
3	505	493.13	517.87	no
4	500	493.13	517.87	no
5	503	493.13	517.87	no
6	497	493.13	517.87	no
7	501	493.13	517.87	no
8	504	493.13	517.87	no
9	499	493.13	517.87	no
10	502	493.13	517.87	no
11	500	493.13	517.87	no
12	496	493.13	517.87	no
13	503	493.13	517.87	no
14	501	493.13	517.87	no
15	513	493.13	517.87	no
16	509	493.13	517.87	no
17	516	493.13	517.87	no
18	511	493.13	517.87	no
19	514	493.13	517.87	no
20	508	493.13	517.87	no
21	512	493.13	517.87	no
22	515	493.13	517.87	no
23	510	493.13	517.87	no
24	513	493.13	517.87	no

Individuals chart · western-electric 4Points 1-14 — 14 consecutive points — all plot below the center line. Each point is a coin flip on a stable process, so eight in a row is about a 1-in-128 run per side. The process mean has most likely moved. Points 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

Individuals chart · western-electric 2Within points 17-19, two of three consecutive points plot more than 2 sigma above the center line. Two points that far out in a window of three is roughly a 1-in-1,000 event for a stable process, and usually means the mean has shifted rather than that the points are unlucky. Points 17, 18, 19.

Individuals chart · western-electric 3Within points 15-19, four of five consecutive points plot more than 1 sigma above the center line. A stable process puts about a third of its points beyond 1 sigma on a given side only 16% of the time, so four in five points to a small sustained shift. Points 15, 16, 17, 18, 19.

Individuals chart · western-electric 3Within points 17-24, four of five consecutive points plot more than 1 sigma above the center line. A stable process puts about a third of its points beyond 1 sigma on a given side only 16% of the time, so four in five points to a small sustained shift. Points 17, 18, 19, 20, 21, 22, 23, 24.

Individuals chart · western-electric 4Points 15-24 — 10 consecutive points — all plot above the center line. Each point is a coin flip on a stable process, so eight in a row is about a 1-in-128 run per side. The process mean has most likely moved. Points 15, 16, 17, 18, 19, 20, 21, 22, 23, 24.

Individuals charts assume the measurements are approximately normal; unlike Xbar charts they get no help from the central limit theorem. Check the distribution (or transform) before acting on marginal signals (Montgomery ISQC 7e §6.4).

Successive moving ranges share an observation and are therefore correlated. Run rules on an MR chart are known to over-signal; interpret anything beyond rule 1 with care (Montgomery ISQC 7e §6.4).

Chart type

This is the decision. The wrong chart still draws.

One measurement per time point — a daily figure, a single reading per batch.

Rule set

More rules means more sensitivity and more false alarms. On rule 1 alone a stable process signals about once every 370 points; the four Western Electric rules bring that down to about 90, so the set signals roughly four times as often where nothing is wrong. Nelson’s eight are more sensitive again.

Your data

One number per line. In time order.

What is measured

How this is calculated

Limits: UCL = D4(2) * MRbar = 3.267 * MRbar; CL = MRbar; LCL = 0 (D3(2) = 0), with sigma estimated as MRbar / d2(2), d2(2) = 1.128.

Limits are 3σ — a convention chosen for its false-alarm rate, not a probability statement. They are computed from the process, never from the specification: a specification limit on a control chart is the single most damaging mistake in SPC, because it invites reacting to every part outside tolerance as though it were a signal.
A variables chart is a pair. The dispersion chart is read first because the location chart’s limits are derived from it.
At least 20 subgroups before the limits are worth much; below that they move substantially as data arrives.
Control chart constants come from one sourced table whose values are verified in CI against their defining identities — including D₃ + D₄ = 2, which holds exactly and caught two transcription errors.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Ch. 6 and Appendix VI; Western Electric (1956), Statistical Quality Control Handbook; Nelson, L.S. (1984), Journal of Quality Technology 16(4).

Save this run to your project

Saved runs can be attached to a project deliverable as evidence. Both what you entered and what the tool computed are stored, so the result can be checked again later.

How this is calculated

Limits are 3 sigma, computed from the process and never from the specification. I-MR estimates sigma as mean moving range / d2(2) = MRbar / 1.128; X-bar R uses Rbar / d2(n) with the A2, D3 and D4 constants from one sourced table whose values are verified in CI against their defining identities, including D3 + D4 = 2. A variables chart is returned as a PAIR and the dispersion chart is rendered first, because the location chart's limits are derived from the dispersion chart's centre line. Western Electric and Nelson rule sets are applied on request, with each violation naming its rule and its citation.

Source: Montgomery, D.C., Introduction to Statistical Quality Control 7e, Ch. 6 and Appendix VI; Western Electric (1956), Statistical Quality Control Handbook; Nelson, L.S. (1984), Journal of Quality Technology 16(4).

Learn the method

Control limits are not specification limitsYellow Belt · 15 min · free