GIFSQ Tools · Module 15 — Metrology, Validation & Laboratory Accreditation · Tool 295 of 500
Apply the Westgard multirule set (1₃ₛ, 2₂ₛ, R₄ₛ, 4₁ₛ, 10ₓ) to a run of control results and get the violation count for each rule — the standard QC decision aid of clinical and food laboratories.
Try sample values — fills the form with the worked example below.
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1₃ₛ violations
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2₂ₛ violations
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R₄ₛ violations
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4₁ₛ violations
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10ₓ violations
Equation: zᵢ = (xᵢ − mean) ÷ SD. 1₃ₛ: one |z| ≥ 3. 2₂ₛ: two consecutive z beyond 2 SD on the same side. R₄ₛ: two consecutive results 4 SD apart. 4₁ₛ: four consecutive z beyond 1 SD on the same side. 10ₓ: ten consecutive results on the same side of the mean.
Method: Westgard multirule procedure (Westgard et al., 1981) as used with Shewhart control charts per ISO 7870-2: 1₃ₛ and R₄ₛ detect random error; 2₂ₛ, 4₁ₛ and 10ₓ detect systematic error. Any violation rejects the run.
Assumptions: the mean and SD are the established control values; results are in run order; the chart is a single-control, single-level chart.
Limitations: the rules assume a stable, normally distributed process; with two control levels the rules apply per level; a rejected run needs a root cause, not just a repeat.
Rounding: violation counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Westgard multirule procedure (Westgard et al., 1981) as used with Shewhart control charts per ISO 7870-2: 1₃ₛ and R₄ₛ detect random error; 2₂ₛ, 4₁ₛ and 10ₓ detect systematic error. Any violation rejects the run.
Assumptions: the mean and SD are the established control values; results are in run order; the chart is a single-control, single-level chart.
Limitations: the rules assume a stable, normally distributed process; with two control levels the rules apply per level; a rejected run needs a root cause, not just a repeat.
Rounding: violation counts are whole numbers; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Mean 10.0 mg/kg, SD 0.2 mg/kg, results 10.1, 10.3, 10.5, 10.7, 10.2, 10.1, 10.3, 10.4, 10.2, 10.1: 1₃ₛ = 1 (10.7), 2₂ₛ = 1 (10.5, 10.7), R₄ₛ = 0, 4₁ₛ = 0, 10ₓ = 1 (all ten above the mean) — run rejected.
Enter values above to see results.
Any rule violation rejects the run: stop, find the cause, correct it, and re-run the affected samples. Tool 295 of 500 — GIFSQ
