Levey-Jennings chart
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.
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.
Why this is not just an individuals chart
The arithmetic is nearly the same. The discipline is not.
On a Shewhart individuals chart the limits are estimated from the readings you plot. On a Levey-Jennings chart the mean and standard deviation are assigned — they come from the QC material's package insert, or from an establishment run of twenty or more results collected when the method was known to be working, and then they are fixed. Every subsequent result is judged against that fixed expectation.
This matters because the failure the chart exists to catch is a slow shift: a reagent lot ageing, a calibrator drifting, a lamp dimming. If the limits are recomputed from the last twenty results, they move with the shift and the chart certifies the drift as normal. It is the same silent failure that spreadsheet control charts have, and in a laboratory the consequence is patient results released against a method that has quietly moved.
The Westgard rules, and what each one implies
James Westgard's 1981 multirule protocol is what makes this chart a decision procedure rather than a picture. The rules are not interchangeable: they split into two families that point at different physical causes.
| Rule | Fires when | Action | Suggests |
|---|---|---|---|
| 1-2s | One result beyond 2SD | Warning only | Nothing on its own — it is the trigger to check the rest |
| 1-3s | One result beyond 3SD | Reject | Random error |
| 2-2s | Two consecutive beyond the same-side 2SD | Reject | Systematic error |
| R-4s | Two consecutive spanning more than 4SD | Reject | Random error |
| 4-1s | Four consecutive beyond the same-side 1SD | Reject | Systematic error |
| 10x | Ten consecutive on the same side of the mean | Reject | Systematic error |
1-2s is a warning, not a rejection, and treating it as one is the classic misapplication. On a well-behaved method roughly one result in twenty falls beyond 2SD by chance alone. Rejecting every one of them means rejecting a working run about five per cent of the time, which in a busy laboratory means repeating work daily for no reason and eventually ignoring the chart. Its correct role is to prompt you to evaluate the other five.
The random-versus-systematic split is the practically useful part. Random error points at imprecision — bubbles, a failing pipette, temperature instability. Systematic error points at a shift in calibration — a new reagent lot, a drifting calibrator, a maintenance event. They send you to different parts of the instrument.
Choosing which rules to run
Every rule you enable adds false rejections. A method with plenty of headroom against its total allowable error does not need the full multirule set — 1-3s alone may be sufficient and will cost you almost no false rejections. A method operating close to its allowable error needs the sensitivity of the full protocol and will pay for it in repeat runs.
That is a judgement about the method's sigma-metric, not a default to be accepted. More rules is not more rigour.
Questions people ask about this
What is a Levey-Jennings chart?
A control chart for a laboratory quality-control material. Each QC result is plotted against an assigned mean, with bands at one, two and three standard deviations either side, and the Westgard rules decide whether the analytical run is acceptable and the patient results in it can be released.
Where do the mean and SD come from?
From the QC material — its package insert, or an in-house establishment run of twenty or more results collected when the method was known to be working. They are then fixed. Recomputing them from the results you are plotting turns the chart into something that cannot detect a shift, because the limits shift with it.
Is 1-2s a rejection?
No. It is a warning, and treating it as a rejection is the most common misapplication of the multirule protocol. On a method that is behaving, about one result in twenty falls beyond 2SD by chance, so rejecting on 1-2s alone means repeating good runs roughly five per cent of the time. Its job is to prompt you to evaluate the other rules.
What is the difference between a Levey-Jennings chart and a control chart?
The arithmetic is nearly identical to a Shewhart individuals chart. The difference is that the mean and SD are assigned in advance rather than estimated from the plotted data, and that the run rules are the Westgard set rather than Nelson or Western Electric.
Which Westgard rules should I use?
It depends on how much headroom the method has against its total allowable error. A method with a high sigma-metric may need only 1-3s and will pay almost nothing in false rejections. A method operating close to its allowable error needs the full multirule set and will pay for that sensitivity in repeat runs. More rules is not more rigour.
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.
More laboratory tools
- 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.
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.
- 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.
- Nelson & Western Electric rules checker — 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.
- 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.
- 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.
- 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.