Plans for acceptance sampling by attributes when observations are destructive

Abstract

The international standard ISO 2859-2 provides plans for acceptance sampling by attributes, that ensure a defined quality level in isolated lots using the hypergeometric distribution. In destructive testing, the sample itself is damaged or changed such that the quality of an entire lot is less relevant than the quality of the lot that remains after removing the sample. Examples include assessing the germination of seeds and the conformity of in-service utility meters. This research highlights that the hypergeometric distribution cannot describe the frequentist consumer's risk of accepting a remaining lot with unsatisfactory quality. Consequently, sampling plans as those provided in ISO 2859-2 are ill-suited to assess the remaining lot when sampling destructively. In contrast, Bayesian statistics inherently infers the lot's quality after sampling. Using a reference prior, we show that sampling plans provided by ISO 2859-2 result in high specific consumer's risk for small remaining lots. The ISO 2859-2 being ill-suited, we design plans for destructive sampling that limit the (Bayesian) specific consumer's risk. To tabulate these plans in a similar way to ISO 2859-2, we propose a new representation that fixes the remaining lot size $N-n$ rather than the sample size $n$. This generalizable, concise and efficient representation is suitable for future standardization of destructive sampling.