sigma_metric: Calculate Six Sigma Metric for Analytical Performance

In valytics: Statistical Methods for Analytical Method Comparison and Validation

Calculate Six Sigma Metric for Analytical Performance

Description

Calculates the sigma metric, which quantifies analytical performance in terms of the number of standard deviations between observed performance and the allowable total error limit. Higher sigma values indicate better performance and lower defect rates.

Usage

sigma_metric(bias, cv, tea)

Arguments

bias	Numeric. Observed bias (systematic error), expressed as a percentage or in the same units as tea.
cv	Numeric. Observed coefficient of variation (imprecision), expressed as a percentage.
tea	Numeric. Total allowable error specification, expressed as a percentage or in the same units as bias.

Details

The sigma metric is calculated as:

\sigma = \frac{TEa - |Bias|}{CV}

Where:

• TEa = Total allowable error (quality specification)

• Bias = Observed systematic error (absolute value used)

• CV = Observed coefficient of variation

Interpretation Guidelines:

The sigma metric provides a standardized way to assess method performance:

• >= 6 sigma: World class performance (<3.4 defects per million)

• >= 5 sigma: Excellent performance (~230 defects per million)

• >= 4 sigma: Good performance (~6,200 defects per million)

• >= 3 sigma: Marginal performance (~66,800 defects per million)

• < 3 sigma: Poor performance (unacceptable defect rates)

Note: These defect rates assume a 1.5 sigma shift (industry standard for long-term process variation).

Value

An object of class c("sigma_metric", "valytics_ate", "valytics_result"), which is a list containing:

sigma

Numeric. The calculated sigma metric value.

input

List with input parameters:

• bias: Observed bias

• cv: Observed CV

• tea: Total allowable error

interpretation

List with performance interpretation:

• category: Performance category (e.g., "World Class", "Good")

• defect_rate: Approximate defect rate per million

Clinical Laboratory Context

In clinical laboratories, a sigma metric of 4 or higher is generally considered acceptable for routine testing, while 6 sigma is the gold standard. Methods with sigma < 3 require stringent QC procedures and may not be suitable for clinical use without improvement.

References

Westgard JO, Westgard SA (2006). The quality of laboratory testing today: an assessment of sigma metrics for analytic quality using performance data from proficiency testing surveys and the CLIA criteria for acceptable performance. American Journal of Clinical Pathology, 125(3):343-354.

Westgard JO (2008). Basic Method Validation (3rd ed.). Westgard QC, Inc.

See Also

ate_from_bv() for calculating TEa from biological variation, ate_assessment() for comprehensive performance assessment

Examples

# Basic sigma calculation
sm <- sigma_metric(bias = 1.5, cv = 2.0, tea = 10)
sm

# World-class performance example
sm_excellent <- sigma_metric(bias = 0.5, cv = 1.0, tea = 8)
sm_excellent

# Marginal performance example
sm_marginal <- sigma_metric(bias = 3.0, cv = 3.0, tea = 12)
sm_marginal

# Using with ate_from_bv() for glucose
ate <- ate_from_bv(cvi = 5.6, cvg = 7.5)
# Assume observed bias = 1.5%, CV = 2.5%
sm <- sigma_metric(bias = 1.5, cv = 2.5, tea = ate$specifications$tea)
sm

# Access the sigma value directly
sm$sigma

valytics documentation built on Feb. 19, 2026, 5:06 p.m.