Bayesian judgment of a dichotomous inspection system when the true state of an evaluated item is unknown

In the quality control of attributes, the evaluation of conforming items is an important task. An inspection system, in a general sense, is not free of errors. Two types are possible: an item is classified as non-conforming when it is conforming, or an item is classified as conforming when it is truly non-conforming. In this paper, a Bayesian method is proposed to judge the efficiency of a new inspection system based on repeated classifications performed on the evaluated items when their true state is not known.