Plans for acceptance sampling by attributes when observations are destructive

2025-08-07

AI Summary

ISO 2859-2 exhibits inaccurate estimation of residual lot quality risk—particularly for small lots—and inflated consumer’s risk in destructive testing due to non-recoverable samples. To address this, this paper proposes a novel Bayesian attribute acceptance sampling method. It innovatively treats the residual lot size as a fixed parameter and integrates a hypergeometric likelihood with a reference prior to construct a decision-theoretic framework that rigorously controls consumer’s risk. The resulting standardized sampling plans are compact and computationally efficient, substantially reducing actual consumer’s risk in small-lot scenarios. This approach extends the applicability of acceptance sampling beyond the limitations of conventional standards in destructive inspection settings. Its theoretical foundation—grounded in objective Bayesian inference—and empirical efficacy support its potential adoption into international standardization frameworks.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• Assessing quality in destructive sampling using ISO 2859-2
• Hypergeometric distribution fails for remaining lot quality
• Designing Bayesian plans for destructive sampling standardization

Innovation

• Bayesian statistics for destructive sampling quality
• New representation fixes remaining lot size
• Generalizable tabulation for future standardization