The inspection of a series of lots from the same producer is a natural field of application of Bayesian approaches. On the one hand, it makes sense to take the posterior of the previous inspection as the prior of the next inspection. On the other hand, such a naive approach can quickly lead to the situation where the prior represents so much accumulated information that new test results from the current lot inspection will hardly have any effect at all on the posterior and, hence, on the calculations of conformance probability, specific consumer risk or expected utility. In other words, a naïve serial implementation of a Bayesian approach could result in such a level of information saturation that any further lot inspection would be meaningless. In effect, such a situation would be similar to having, e.g., complete trust in the producer and accepting all lots on faith. For this reason, it is important to carefully consider exactly how the conformance probability or the utility approach is applied in practice. The present paper describes a fully developed procedure for implementing these two approaches in connection with serial lot inspection. In this approach, a data-ageing procedure is described. The basic principle is to downweight older data in such way as to prevent information saturation in the sense of over-informative priors. Moreover, when the sample size, the expected value for the proportion nonconforming and the inspection frequency are constant, it is possible to derive closed expressions for the expected values of the hyperparameters. These, in turn, allow a pragmatic approach for the specification of inspection frequency or sample size.
Uhlig et al. (Mon,) studied this question.