On Bayesian power analysis in reliability

Evaluation of reliability of a production process is a crucial step in sustainability assessment. In this article we consider the sample size determination problem when time-to-failure is modeled by a Rayleigh distribution. Following a hybrid Bayesian-frequentist approach, the selection of the number of units is based on the so-called probability of success (PoS) of the experiment, that is the expected value of the power function with respect to a design prior distribution for the mean failure time. This method works properly only if PoS is a representative summary of the distribution of the power function induced by the design prior. Therefore we derive and analyze the density of the power function for one-sided tests on the Rayleigh parameter, using conjugate design priors. Numerical examples are discussed.