Biostatistics & Epidemiology
Westgard Six-Sigma Laboratory Quality Metric: (TE_a% - |Bias%|) / CV% & QC Rules
Evaluate clinical analyzer analytical performance and select optimal Westgard Statistical Quality Control (SQC) rules using James O. Westgard’s Sigma-Metric equation Sigma = (TE_a% - ABS(Bias%)) / CV%.
Combine CLIA Total Allowable Error (TE_a), Method Bias, and Imprecision (CV) into one Six-Sigma score!
In clinical chemistry, hematology, and immunoassay laboratories, CLIA / CAP / Ricos biological-variation standards specify a maximum tolerable Total Allowable Error TE_a (%) for every analyte (e.g., Serum Potassium or Glucose TE_a = 8%–10%, HbA1c TE_a = 6%)! Formulated by clinical chemist James O. Westgard, the Analytical Sigma-Metric counts how many assay Standard Deviations (CV%) fit inside the remaining error budget after subtracting systematic trueness offset ABS(Bias%): Sigma = (TE_a% - ABS(Bias%)) / CV%!
High-Sigma assays (>= 6.0 Sigma, "World Class" < 3.4 defects per million) need only a single wide 1_3s control rule with N = 2 QC levels per run (minimizing costly false QC rejections!), whereas 4.0 to < 5.0 Sigma requires multi-rule 1_3s / 2_2s / R_4s / 4_1s monitoring, and < 3.0 Sigma indicates marginal/unacceptable analytical stability requiring recalibration or method replacement!
| Assay Analytical Sigma Band | Defect Rate & Performance Tier | Recommended Westgard QC Rule Strategy |
|---|---|---|
| Sigma >= 6.0 | World-Class Six-Sigma | Single 1_3s rule (N = 2 QC measurements, minimal false alarms) |
| 5.0 <= Sigma < 6.0 | Excellent Analytical Margin | 1_3s / 2_2s / R_4s (N = 2) |
| 4.0 <= Sigma < 5.0 | Moderate Clinical Margin | 1_3s / 2_2s / R_4s / 4_1s (N = 4) |
| Sigma < 3.0 | Unacceptable Defect Rate | Max multi-rule QC + root-cause recalibration / reagent audit |
Westgard Analytical Sigma-Metric (TE_a% - ABS(Bias%)) / CV%
Evaluates (B2 - ABS(B3)) / B4 across Total Allowable Error TE_a% (B2 > 0), signed %Bias from peer/reference target (B3), and analytical Coefficient of Variation CV% (B4 > 0).
=IF(OR(B2 <= 0, B4 <= 0), "Requires TE_a% > 0 and Analytical CV% > 0", ROUND((B2 - ABS(B3)) / B4, 2))Westgard SQC Rule Tier Selection from Assay Sigma Score
Maps Assay Sigma directly onto Westgard’s Sigma-SQC rule-selection protocol.
=IF(OR(B2 <= 0, B4 <= 0), "Requires TE_a% > 0 and Analytical CV% > 0", IF((B2 - ABS(B3)) / B4 >= 6, "Sigma >= 6.0: World-Class (Single 1_3s Rule, N=2)", IF((B2 - ABS(B3)) / B4 >= 5, "5.0–5.99 Sigma: Excellent (1_3s / 2_2s / R_4s, N=2)", IF((B2 - ABS(B3)) / B4 >= 4, "4.0–4.99 Sigma: Moderate (1_3s / 2_2s / R_4s / 4_1s, N=4)", IF((B2 - ABS(B3)) / B4 >= 3, "3.0–3.99 Sigma: Marginal (Full Multi-Rule + Frequent QC)", "Sigma < 3.0: Unacceptable — Recalibrate / Investigate Method")))))Try the example
Use the original values or change them to test your understanding.