Using posterior information about the distribution of failure time parameter in acceptance sampling schemes

In a classical acceptance sampling scheme, sample test data is used to construct a hypothesis test for the specified parameter. If the hypothesis is not rejected and the sample is accepted, the distribution of the quality characteristic can be calculated from the null distribution. When a Bayesian procedure is employed, acceptance criteria are not so easy to establish. Relation between a posterior distribution for the parameter and the likely distribution of the quality characteristic of individual items will be studied in the paper. We propose computing the post-posterior distribution of a given quality characteristic, and setting acceptance criteria in terms of this distribution. Further we propose computing the posterior consumer's risk in a situation of reliability demonstration testing. Results and derivations will be given in the case where the number of nonfunctioning items in a production lot is the quality characteristic of interest. Acceptance sampling for a normally distributed quality characteristic is discussed, suppose the required specification limits for this characteristic are μ ± kσ. If the test scheme is fixed by the number of failures and total test time, suppose that a product's reliability specification is in terms of failure rates, posterior risk is discussed for two situations dependently on consumer's demands.