Westgard Rules Interpreter
Westgard Rules Interpreter
Enter this run’s control result as a standard deviation index and answer five questions about the recent history. The page names the Westgard rule violated and says whether the run should be rejected.
Westgard Rules
SDI + run history → ruleToday’s control sits at +2.4 SD. The previous control was within 1 SD, the other control in the run is within 2 SD, the last four are not all beyond 1 SD on one side, and the last ten are not all on one side
The rule set
1-3s — one control beyond 3 SD → reject
2-2s — two consecutive beyond the same 2 SD limit → reject
R-4s — range within a run exceeds 4 SD → reject
4-1s — four consecutive beyond the same 1 SD limit → reject
10x — ten consecutive on the same side of the mean → reject
- 1-2s
- a warning, and the most misused rule in the laboratory. About 5% of results from an in-control method fall beyond 2 SD by definition, so rejecting on 1-2s alone throws away roughly one run in twenty per control — one in ten with two controls. Its purpose is to trigger inspection of the rejection rules, nothing more
- 1-3s
- the main rejection rule. A single control beyond 3 SD happens by chance about once in 370 results, so it is a specific signal of a large error. On a method with high sigma it is very nearly sufficient on its own
- 2-2s
- two consecutive controls beyond the same 2 SD limit — the same side, not just the same magnitude. Detects systematic error: a shift in calibration, a new reagent lot, a maintenance event
- R-4s
- a range of more than 4 SD between two controls within one run, typically one above +2 SD and one below −2 SD. Detects random error — imprecision rather than bias — and is applied within a run
- 4-1s
- four consecutive controls beyond the same 1 SD limit. Detects a small systematic shift that no single point would reveal
- 10x
- ten consecutive controls on the same side of the mean, however close. Detects a shift in the mean itself. Some laboratories use 8x or 9x, and some apply it across both control levels together
- how many rules to use
- as few as the method’s sigma allows. A method at 6 sigma is adequately controlled by 1-3s with two controls; a method at 3 to 4 sigma needs the full multirule procedure with four controls and will still detect error poorly. Adding rules to a high-sigma method buys false rejections rather than safety
Worked example
Today's control sits at +2.4 SD. The previous control was within 1 SD, the other control in the run is within 2 SD, the last four are not all beyond 1 SD on one side, and the last ten are not all on one side
|+2.4| is not ≥ 3, so 1-3s has not fired
The preceding control was not beyond the same 2 SD limit → no 2-2s
No control in the run sits below −2 SD, so the within-run range is under 4 SD → no R-4s
The last four are not all beyond 1 SD on the same side → no 4-1s; the last ten are not all on one side → no 10x
|+2.4| is ≥ 2, so the only rule met is 1-2s — a warning. Accept the run
Change one answer — say the previous control was also beyond +2 SD — and the same +2.4 becomes a 2-2s violation and a rejection. The current result has not changed at all; what changed is what came before it
What each rule detects, and what it costs
| Rule | Action | Detects | False rejection on its own |
|---|---|---|---|
| 1-2s | Warning only | Nothing specific — it is a trigger to inspect | ≈ 5% per control per run |
| 1-3s | Reject | Large random or systematic error | ≈ 0.3% per control per run |
| 2-2s | Reject | Systematic error — a shift | Low |
| R-4s | Reject | Random error — imprecision | Low |
| 4-1s | Reject | A small systematic shift | Low |
| 10x | Reject | A shift in the mean, including slow drift | Low |
How many rules a method actually needs
| Sigma | Controls per run | Rules | Why |
|---|---|---|---|
| ≥ 5 | 2 | 1-3s alone | The method has so much room that a large error is needed before an unacceptable result can be produced, and 1-3s catches large errors |
| 4–5 | 2 | 1-3s / 2-2s / R-4s | Error detection now needs help, and these three cover large error, shift and imprecision between them |
| 3–4 | 4 | 1-3s / 2-2s / R-4s / 4-1s / 10x | The full multirule procedure, more controls, and a shorter interval between QC events — and error detection is still imperfect |
| < 3 | — | No design is adequate | Fix the bias, fix the imprecision or change the method. Rules cannot rescue a method with no headroom |
Why 1-2s is a warning and not a rejection
The multirule procedure published by Westgard and colleagues in 1981 replaced a simple question — is this control result beyond 2 SD — with a set of six patterns, each tuned to a different kind of failure. The reason is arithmetic rather than fashion. If a method is behaving perfectly, about 5% of its control results will fall beyond 2 SD, because that is what 2 SD means. A laboratory running two controls per run and rejecting whenever either exceeds 2 SD therefore discards roughly one run in ten with nothing at all wrong with it, and pays for that in repeat testing, delayed reports and, eventually, in staff who stop believing the control chart.
So 1-2s was demoted to a warning. Its job is to make somebody look at the chart, and what they look for is one of the rejection rules. The 1-3s rule catches a single large excursion: a control beyond 3 SD happens by chance about once in 370 results, so it is a specific signal. The 2-2s and 4-1s rules catch systematic error — two consecutive points beyond the same 2 SD limit, or four beyond the same 1 SD limit — where the information is in the direction rather than the size. The 10x rule catches a shift in the mean even when every individual point is comfortably inside the limits, which is what slow drift looks like. And the R-4s rule catches the opposite failure: one control above +2 SD and another below −2 SD in the same run is a range of more than 4 SD and means the method has become imprecise, not biased.
Reading the pattern also tells you where to look. A shift — 2-2s, 4-1s, 10x — is usually calibration, a reagent or calibrator lot, or a maintenance event, and it normally has a moment you can point to on the chart. Random error — R-4s, or a 1-3s with the other control fine — is usually mechanical or physical: bubbles, a partly blocked probe, poor mixing, an unstable temperature, a control vial that has been thawed too often.
The last point is the one most often missed. How many rules you should run is not a matter of thoroughness but of the method’s sigma. A method with 6 sigma of headroom is adequately controlled by 1-3s with two controls per run, and every rule added to it detects nothing while generating false rejections. A method at 3 to 4 sigma needs the whole procedure, four controls and a shorter QC interval, and will still miss errors that matter. Calculate the sigma first; the QC design follows from it. And remember what quality control cannot see at all: a control chart in perfect order says nothing about a haemolysed sample, a clot or a tube labelled with the wrong patient’s name.
Frequently asked questions
Why is 1-2s only a warning?
Because about 5% of control results from a method working perfectly fall beyond 2 SD — that is the definition of 2 SD. Rejecting on 1-2s alone gives a false-rejection rate of roughly 5% per control per run, so a laboratory with two controls throws away about one run in ten for nothing. The rule’s job is to trigger inspection of the rejection rules.
Which Westgard rules should I actually use?
As few as the method’s sigma metric allows. At 5 sigma or above, 1-3s with two controls per run is sufficient. At 4 to 5 sigma, add 2-2s and R-4s. At 3 to 4 sigma you need the full procedure with four controls. Below 3 sigma no rule set is adequate and the method itself has to change.
What is the difference between 2-2s and R-4s?
Direction. 2-2s is two consecutive controls beyond the same 2 SD limit — the same side — and indicates systematic error, a shift in calibration. R-4s is one control above +2 SD and another below −2 SD within the same run, a range of more than 4 SD, and indicates random error, meaning the method has become imprecise.
Should a violation always mean rejecting the run?
Every rule except 1-2s is a rejection rule, and the safe default is to hold the results and investigate. Some laboratories downgrade 4-1s and 10x to warnings on very high-sigma methods, on the grounds that the error those rules detect is far too small to change a clinical decision there. That is a defensible local decision, but it should be written down and justified against the method’s sigma, not made run by run.
Does good quality control mean the patient results are correct?
No. Quality control monitors the analytical system across the run. It cannot detect anything about an individual specimen — haemolysis, a clot, a short sample, contamination from a drip arm, or a mislabelled tube — and those pre-analytical problems are a far commoner cause of a wrong result than a method going out of control.
Related calculators
References
- Westgard JO, Barry PL, Hunt MR, Groth T. A multi-rule Shewhart chart for quality control in clinical chemistry. Clin Chem. 1981;27(3):493–501.
- Westgard JO. Basic QC Practices. 4th ed. Westgard QC; 2016.
- CLSI C24-Ed4. Statistical Quality Control for Quantitative Measurement Procedures: Principles and Definitions. 4th ed. Clinical and Laboratory Standards Institute; 2016.
- Westgard JO, Westgard SA. Six Sigma quality management system and design of risk-based statistical quality control procedures. Clin Lab Med. 2017;37(1):85–96.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.