Simulation-based designs for accelerated life tests

In this paper we present a Bayesian decision theoretic approach to the design of accelerated life tests (ALT). We discuss computational issues regarding the evaluation of expectation and optimization steps in the solution of the decision problem. We illustrate how Monte Carlo methods can be used in preposterior analysis to find optimal designs and how the required computational effort can be avoided by using curve-fitting techniques. In so doing, we adopt the recent Monte-Carlo-based approaches of Muller and Parmigiani (1995. J. Amer. Statist. Assoc. 90, 503–510) and Muller (2000. Bayesian Statistics 6, forthcoming) to develop optimal Bayesian designs. These approaches facilitate the preposterior analysis by replacing it with a sequence of scatter plot smoothing/regression techniques and optimization of the corresponding fitted surfaces. We present our development by considering single and multiple-point fixed, as well as, sequential design problems when the underlying life model is exponential, and illustrate the implementation of our approach with some examples.