Paste your data, get every rule violation explained

Every run rule evaluated on your data, each violation named in plain English with what it usually indicates — a shift, a trend, tool wear, two machines mixed.

How you check run rules in Excel

There is nothing built in, so each rule becomes its own helper column. The zone tests are nested IFs against sigma bands, the run tests are COUNTIFs over a trailing window, and rule 4 — fourteen points alternating up and down — takes a genuine effort to express as a formula at all.

Eight rules is eight columns of formulas that nobody but their author can read, and all of them break silently the moment somebody inserts a row in the middle. The failure mode is not an error in a cell; it is a rule that stops firing and gives you a clean chart.

Nothing you paste leaves this calculation. It is not stored, not logged and not sent anywhere else — the numbers are computed and returned, and that is all. Paste straight out of a spreadsheet — tab-separated columns are understood as they land.

What the rules are for

A point outside the control limits is the obvious signal, and the least useful one: by the time it fires, the part is already made. The run rules exist to catch the process moving while everything is still inside the limits — a shift, a drift, a mixture of two machines — which is where the money is.

Nelson or Western Electric?

Western Electric's handbook (1956) defined four zone tests. Nelson's set (1984) keeps those and adds four more, renumbered — which is why the same test has two names:

Western Electric	Nelson	The test
1	1	One point beyond 3σ
2	5	2 of 3 beyond 2σ, same side
3	6	4 of 5 beyond 1σ, same side
4	2	8 in a row on one side of the centre line

Pick Western Electric above and the findings are numbered their way, with the Nelson number in brackets. The one place the standards genuinely differ is that last test — Western Electric uses eight consecutive points, Nelson uses nine — and this checker evaluates nine in both modes, so its Western Electric view is very slightly less sensitive than the handbook. It says so on the finding rather than quietly relabelling one standard as the other.

The part most people get wrong

Running all eight rules is usually a mistake. Each rule has its own false alarm rate, and together they fire often enough on healthy data to train people to ignore the chart. The zone rules (5–8) also assume the data is roughly normal and that consecutive readings are independent — on a fast-sampled sensor they fire constantly and mean nothing. Pick the rules that match your process, and be able to say why each one is on.

And the limits must be frozen. If they were computed from the same window you are checking, a drifting process drags them along and the rules never fire at all. This tool computes limits from the data you paste, which is right for a one-off look and wrong for a live process — see the control limit calculator for why.

What the Excel version will not do

A broken rule looks exactly like a stable process: Formulas that no longer reference the right window return FALSE. The chart shows no violations, which is precisely what you were hoping to see.
The rules depend on the zones, which depend on the limits: If the limits recalculate as data arrives, the sigma zones move with them, and the zone rules are evaluating against boundaries that were different yesterday.
Knowing a rule tripped is not the same as being told: Run rules exist to catch a process going wrong before it makes scrap. Value that arrives when someone next opens the file has mostly expired.

Questions people ask about this

What are the Nelson rules?

Eight tests for patterns in a control chart that are unlikely to occur by chance: one point beyond three sigma, nine points on one side of the centre line, six rising or falling, fourteen alternating, two of three beyond two sigma, four of five beyond one sigma, fifteen hugging the centre line, and eight with none near it. Each one points at a different kind of cause.

What is the difference between Nelson and Western Electric rules?

Western Electric's handbook defined four zone tests; Nelson kept those and added four more, renumbering them. Western Electric rule 2 is Nelson rule 5, and rule 3 is Nelson 6. The one genuine difference is the shift test: Western Electric uses eight consecutive points on one side of the centre line, Nelson uses nine.

Should I run all eight rules?

Usually not. Every rule carries its own false-alarm rate, and together they fire often enough on healthy data to train people to ignore the chart. The zone rules also assume roughly normal, independent readings — on a fast-sampled sensor they fire constantly and mean nothing. Choose the rules that match your process and be able to say why each is on.

What does a rule violation actually mean?

That the pattern is unlikely to be chance, not that a part is bad. Nine points on one side means the average has moved; six rising means something is drifting, like tool wear or a bath heating; fourteen alternating usually means two things are being charted as one. Each finding here says what the pattern is and what it typically indicates.

Want this to keep itself up to date?

A calculator answers for the data you pasted. A control chart answers for the data your line produced this morning — limits frozen at a baseline you locked, rules evaluated on every new reading, an alert when one trips.

Start now See it on live data

More control charts tools

Control limit calculator — Give it subgroups or individual readings and it returns the control limits for the chart, the range or sigma chart beneath it, and every constant it used to get there.
Control chart generator — Paste a column of numbers, or rows of subgroups, and get a real control chart: limits from the data, Nelson rules 1–4 evaluated, out-of-control points marked.
X̄-R chart calculator — Subgroups in, X̄ and R charts out — limits from A₂, D₃ and D₄, run rules evaluated, and the range chart shown first because it decides whether the averages chart can be trusted.
X̄-s chart calculator — For subgroups big enough that the range wastes them. Limits from A₃, B₃ and B₄, sigma recovered with the c₄ correction, and the s chart read first because it decides whether the averages chart can be trusted.
I-MR chart calculator — For processes that give you one number at a time — a batch, an oven, a destructive test. Limits from the mean moving range, run rules evaluated, and an honest note about what an individuals chart cannot see.
p, np, u and c chart calculator — Counted data rather than measured: proportion defective, number defective, defects per unit. Limits that step with the sample size instead of pretending it never changed, and an honest warning when the counts are too low for three-sigma limits to mean anything.

Everything else

Cp / Cpk calculator — Paste measurements — or type a mean and a sigma — with your tolerance, and get Cp, Cpk, Pp, Ppk, the sigma level and the expected parts per million out of spec.
Cpk confidence interval & sample size — A Cpk of 1.33 from 30 pieces has a 95% interval of roughly 0.97 to 1.69. See the uncertainty in your own number, and how many parts would settle it.
Cpk ↔ PPM ↔ sigma level converter — What PPM is a Cpk of 1.33? What Cpk does 3.4 PPM need? Both conventions shown side by side, because the 1.5 sigma shift is why two sources disagree by a factor of ten.
Control chart constants — The whole table, n = 2 to 25, with the formula each constant belongs to. The same values the charts on this site are computed from.
Levey-Jennings chart with Westgard rules — Paste your QC results with the assigned mean and SD from the package insert, and get the chart with every sigma band drawn and all six Westgard rules evaluated — each one named, and labelled random or systematic error.
Bland-Altman plot — Paired readings from two methods, plotted as difference against average — with the bias, the limits of agreement, their confidence intervals, and a test for whether the disagreement depends on the magnitude.
Pareto chart generator — Categories and counts in, ranked bars and the cumulative line out — with the vital few named, an "Other" bucket that always sorts last, and an honest warning when the distribution is flat and there is no dominant cause to attack.
Box and whisker plot generator — One column per group, boxes side by side. Quartiles, the 1.5×IQR fences, whiskers that stop at real readings and outliers drawn individually — with the quartile method stated, because that is why your plot and Excel's disagree.
Histogram and normality test — A histogram with the fitted normal curve, both standard bin rules with a reasoned recommendation, and an Anderson-Darling test that refuses to tell you your data is normal — because no test can.
Gage R&R calculator (ANOVA) — Paste a crossed study — part, operator, reading — and get the full ANOVA: repeatability and reproducibility separated, the part-by-operator interaction tested rather than assumed away, %GRR, %Tolerance and ndc against AIAG's bands.
Grubbs outlier test — The G statistic against its critical value, the p-value, and the point implicated — plus a straight answer about what to do next, which is almost never to delete the reading.
Scatter diagram and correlation — Paired readings plotted, with Pearson r, Spearman rho, r², the least-squares line and its p-value — and the two reported together, because when they disagree the disagreement is the finding.
Standard deviation calculator — The usual summary statistics, and the thing a spreadsheet will not tell you: the within-subgroup sigma a control chart uses, beside the overall sigma a textbook means. The gap between them is why Cpk and Ppk disagree.