Quality Systems
Two defects in 420 pieces proves far less than it reads.
— %
The reduction the verification sample actually proves at the chosen confidence
The Wilson score limit assumes independent units. Textile nonconformities are rarely independent - they cluster by lot, operator, machine, shift and supplier delivery - so a verification sample drawn from two lots is narrower on paper than it is in truth, and the demonstrated reduction should be read as optimistic when the sample came from few sources. The baseline is treated as a known constant, which is defensible only while the baseline sample is several times the verification sample; when the two are comparable, use a two-proportion test or a Fisher exact test instead, and expect the defensible reduction to fall further. Never take a baseline from a single bad week: regression to the mean will hand you an improvement no action caused. Below about five expected defects the exact Clopper-Pearson limit is slightly more conservative than Wilson and is the safer choice for a regulatory nonconformity. Units needed to prove the target caps at 1,000,000 and the days figure at 36,500 when the observed rate is at or above the target rate, since no sample size proves the target in that case. The days figure assumes the verification inspection rate continues unchanged, and it is a floor rather than a plan: a window must also span a full rotation of shifts, operators, lots and machines, because sample size alone does not create representativeness. Costs are per unit in any single currency, and the saving is deliberately booked at the proven rate rather than the observed one.
Corrective & Preventive Action Effectiveness Tracker — free, with the formula and a worked example, at Textile School.