A Bayesian Method for Planning Accelerated Life Testing

In this paper, a Bayesian criterion is proposed based on the expected Kullback-Leibler divergence between the posterior and the prior distributions of the parameters of interest. We call the Bayesian criterion the reference optimality criterion, which is to find an optimal plan to maximize the amount of information from the data. A large-sample approximation is utilized to simplify the formula to obtain optimal plans numerically. Because optimal plans based on reference optimality criterion do not depend on the sample size, a modified reference optimality criterion is proposed. We give numerical examples using the Weibull distribution with type I censoring to illustrate the methods, and to examine the influence of the prior distribution, censoring time, and sample size. We also compare our methods with other criteria through Monte Carlo simulation.