Reference optimality criterion for planning accelerated life testing

• A new Bayesian optimal criterion is proposed.
• Large-sample approximation and Monte Carlo simulation algorithm are used to find the optimal designs.
• We compare our criterion with other criteria via several examples.

Most of the current literatures on planning accelerated life testing are based on D-optimality criterion and V-optimality criterion. Such methods minimize the generalized asymptotic variance of the maximum likelihood estimators of the model parameters or that of a quantile lifetime. Similarly, the existing Bayesian planning criterion is usually based on the posterior variance of a quantile lifetime. In this paper, we present a framework for a coherent approach for planning accelerated life testing. Our approach is based on the expectation of Shannon information between prior density function and posterior density function, which is also the spirit for deriving reference prior in Bayesian statistics. Thus, we refer to the criterion as the reference optimality criterion. Then the optimal design is selected via the principle of maximizing the expected Shannon information. Two optimization algorithms, one based on large-sample approximation, and the other based on Monte Carlo simulation, are developed to find the optimal plans. Several examples are investigated for illustration.