On the Probability of Success of a Reliability Experiment

Evaluation of reliability of a production process is a critical issue 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 unknown parameter (the mode of the failure time distribution). This method works properly only if PoS is a representative summary of the distribution of the power function induced by the design prior. Using conjugate design priors, we obtain the explicit expression for the density of the power function for one-sided tests on the Rayleigh parameter. The non-conjugate case is addressed via simulation. When the shape of the density of the power suggests that PoS is not adequate, an alternative summary is proposed, yielding a probability criterion for sample size determination. An application to time-to-failure of an air conditioning system is used for illustration.