Acceptance Sampling Plans Based on Utility Functions—Inspection of Lots and Processes by Attributes

• DOI: 10.20944/preprints202504.1544.v1
• Publication Date: 2025-04-22T00:22:03Z
• Authors: Steffen Uhlig; Bertrand Colson; Rainer Göb; Francesca Pennecchi; Sam Ellis; Mike Hicks; John Vandenbemden; Roger Kissling; Petra Gowik

In the ISO 2859 and ISO 3951 series, the acceptance sampling plans have relatively large sample size values. For this reason, it is interesting to develop an approach to acceptance sampling based on Bayesian statistics. In the present paper, this focus is on Bayesian plans developed from the perspective of utility, understood as benefits minus costs. This focus on utility rather than on risk allows a completely different approach to acceptance sampling plans to be developed. The utility is defined via three simple parameters and it is shown how sample size and acceptance number can be calculated by maximizing utility. The calculation is further refined via a hierarchical model which tests the prior distribution against the empirical data. Finally, tables of standard plans are provided for the practitionner.