Acceptance Sampling

When 100% inspection is impractical or destructive (tensile testing, burst pressure, shelf life), acceptance sampling provides a statistically grounded accept/reject decision. Standards like ANSI/ASQ Z1.4 (attribute) and Z1.9 (variable) define sampling plans based on lot size, acceptable quality level (AQL), and desired protection against bad lots.

Variable sampling plans (Z1.9) are more efficient than attribute plans because they use measurement data rather than pass/fail counts, requiring smaller sample sizes for the same protection. However, Z1.9 plans assume normally distributed measurements — a critical limitation when dealing with non-normal quality characteristics.

The consequences of a poor sampling plan are asymmetric: accepting a bad lot reaches the customer and creates quality escapes, recalls, or warranty claims. Rejecting a good lot wastes material and delays shipments. Getting the sampling plan right — with accurate distribution assumptions — directly impacts both quality risk and operational efficiency.

EntropyStat improves variable acceptance sampling by removing the normality assumption from lot quality estimation. Traditional Z1.9 plans estimate the fraction nonconforming from the sample mean and standard deviation, assuming a normal distribution to extrapolate tail probabilities. When measurements are non-normal, this extrapolation can significantly overstate or understate the true defect rate.

Using the EGDF to estimate the lot's distribution directly from sample measurements produces more accurate fraction-nonconforming estimates. The EGDF captures the actual tail behavior — whether skewed, heavy-tailed, or truncated — so the accept/reject decision is based on realistic defect probability rather than a Gaussian approximation.

The EGDF's ability to produce stable estimates from small samples also enables tighter sampling plans. If 5–8 measurements can characterize the lot distribution reliably, the required sample size for a given discrimination ratio (consumer risk vs. producer risk) may be smaller than what Z1.9 tables require — reducing inspection costs without sacrificing quality protection.