Abstract: For problems in the fault detection rate (FDR) field statistics verification test occurred when the field usage data for testability of equipment with high reliability is small sample, the Bayes inference on dynamic population-based FDR field statistics verification model and method are considered and launched. Firstly, an ordinal relation model of FDR at different stages is founded, a Bayes fusion method based on the Dirichlet prior distribution is studied, and a Bayes point estimation and the lower confidence limit on FDR in service are gained by fusing the expert experience, the test information at every stage and the field usage information. A method based on experts experience for determining the Dirichlet prior distribution parameters is given. Then, the Gibbs sampler is used to solve high dimensional integrals from which the posterior inference of FDR can be computed. Finally, The study demonstrates the FDR statistics verification by means of such model can produce the evaluation conclusion with high confidence level in a short field usage period and provide theory base for the research of field statistics verification for equipment with high reliability.

Key words: testability, reliability, field statistics verification, small sample, Bayes, Dirichlet distribution, Markov chain Monte Carlo methods, Gibbs sampler