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