Sigma Metric Calculator
Sigma Metric Calculator
Combine allowable total error, bias and imprecision into a single figure for how much room a method has — and let that figure decide how many controls you run and which rules you apply.
Sigma Metric
TEa, bias, CV → sigmaGlucose: TEa 10%, bias 1.5%, CV 2.5%
Formula
≥6 world class · 5–6 excellent · 4–5 good · 3–4 marginal · <3 unacceptable
- TEa
- allowable total error as a percentage — the room the method is given. It is a chosen specification, not a measurement, so two laboratories can compute different sigmas for identical performance simply by choosing different sources. Always state which you used
- |bias|
- systematic error, taken as its absolute size because a shift in either direction eats the same amount of room. Bias is subtracted before the division, so it is the more damaging of the two error types: it consumes the budget outright rather than being averaged out
- CV
- random error, from your own long-term QC near the decision level. Sigma is literally how many standard deviations fit between the method's mean result and the edge of what is allowable
- the level matters
- a method usually has a different sigma at each QC concentration, because both bias and CV change across the range. Calculate it at the level nearest the clinical decision point, and quote the concentration with the result
- what it decides
- the number of controls and the rules applied to them. A high-sigma method is safe with a single 1-3s rule and two controls; a marginal one needs a full multirule procedure and four, and still detects error less well
Worked example
Glucose: TEa 10%, bias 1.5%, CV 2.5%
10.0 − |1.5| = 8.5% of room left after bias
8.5 ÷ 2.5 = 3.4 sigma
Marginal: this needs a full multirule procedure with four controls per run, and will still reject occasionally without a real error present
Now remove the bias by recalibrating: 10.0 ÷ 2.5 = 4.0 sigma, which drops the requirement to a 1-3s/2-2s/R-4s multirule with two controls
Halving the CV instead, to 1.25% with the bias untouched, gives 8.5 ÷ 1.25 = 6.8 sigma. Both routes help, but bias is subtracted while imprecision divides — which is why the same percentage of bias and CV are not equally expensive
What each sigma level costs in quality control
| Sigma | Verdict | Controls per run | Rules |
|---|---|---|---|
| ≥ 6 | World class | 2 | 1-3s alone |
| 5–6 | Excellent | 2 | 1-3s alone |
| 4–5 | Good | 2 | 1-3s / 2-2s / R-4s |
| 3–4 | Marginal | 4 | 1-3s / 2-2s / R-4s / 4-1s, with a shorter QC interval |
| < 3 | Unacceptable | — | No design is adequate; fix or replace the method |
Bias and imprecision are not equally expensive
| Change | TEa | Bias | CV | Sigma |
|---|---|---|---|---|
| Starting point | 10% | 1.5% | 2.5% | 3.4 |
| Recalibrate away the bias | 10% | 0% | 2.5% | 4.0 |
| Halve the imprecision | 10% | 1.5% | 1.25% | 6.8 |
| Both | 10% | 0% | 1.25% | 8.0 |
| Choose a stricter TEa instead | 7.5% | 1.5% | 2.5% | 2.4 |
One number that decides how much QC you need
The sigma metric asks a simple question: how many standard deviations of the method's own scatter fit between where its results actually sit and the edge of what would be an unacceptable result? Take the allowable total error, subtract the bias — because a systematic shift has already used up part of the budget before any random scatter is considered — and divide what remains by the CV. A glucose method with a 10% allowable total error, 1.5% bias and 2.5% CV has 8.5% of room and a CV of 2.5%, giving 3.4 sigma.
The scale is borrowed from manufacturing, where six sigma corresponds to about 3.4 defects per million. In the laboratory the reading is conventional: 6 or above is world class, 5 to 6 excellent, 4 to 5 good, 3 to 4 marginal, and below 3 unacceptable. The useful thing is that the number is not a grade but an instruction. A method at 6 sigma is safe with a single 1-3s rule and two controls per run. At 4 to 5 it needs a 1-3s/2-2s/R-4s multirule with two controls. At 3 to 4 it needs a full multirule procedure with four, and it will still both miss real errors and reject good runs more often than anyone would like. Below 3, no arrangement of rules rescues it, and the effort belongs on the method itself.
That inverts the way quality control is often planned. Running the same two controls and the same rules on every analyte spends the same effort on a method with enormous headroom and one with almost none. Sigma says where the effort should go, and it also says when more QC is the wrong answer: adding rules to a high-sigma method produces false rejections, repeat runs and delayed reports without detecting anything.
Two cautions. Bias and imprecision are not interchangeable, because bias is subtracted while imprecision divides — in the example above, recalibrating away 1.5% of bias buys 0.6 sigma while halving the CV buys 3.4. And the allowable total error is a choice, not a measurement: biological-variation-based specifications, regulatory limits and EQA criteria can differ by a factor of two for the same analyte, and every sigma metric moves with them. Quote the source of your TEa and the concentration you calculated at, or the number cannot be compared with anyone else's.
Frequently asked questions
How is the sigma metric calculated?
Subtract the absolute bias from the allowable total error, both as percentages, then divide by the CV. A method with 10% allowable total error, 1.5% bias and 2.5% CV gives (10 − 1.5) ÷ 2.5 = 3.4 sigma.
What is a good sigma metric?
Six or above is world class, 5 to 6 excellent, 4 to 5 good and 3 to 4 marginal. Below 3 is unacceptable, because no practical quality control design detects the errors such a method makes without rejecting a great many good runs as well.
How does sigma decide my QC design?
A high-sigma method needs little: a single 1-3s rule with two controls per run. As sigma falls, error detection has to come from more rules and more controls — a multirule procedure with two controls at 4 to 5 sigma, four controls at 3 to 4 — and below 3 the method itself needs fixing.
Where does allowable total error come from?
From a chosen specification: a biological-variation-derived goal, a regulatory limit such as CLIA, or an EQA scheme's acceptance criteria. These can differ substantially for the same analyte, so a sigma metric is only comparable between laboratories when both state which source they used.
Why does bias matter more than imprecision?
Because it is subtracted from the allowable error before the division, so it removes headroom outright rather than being averaged away by repeated measurement. Removing a bias by recalibration is often the quickest way to raise a marginal sigma, and it is usually cheaper than improving imprecision.
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References
- 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.
- 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.
- CLSI EP15-A3. User Verification of Precision and Estimation of Bias; Approved Guideline. 3rd ed. Clinical and Laboratory Standards Institute; 2014.
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.