Optimal allocation of test positions and testing time in a factorial life testing experiment

This paper describes how to plan an "optimal" life testing experiment when the lifetime is assumed to have an exponential distribution. We further assume that the mean lifetime is equal to exp([beta]1x1 + ... + [beta]kxk) where the covariates xi form an orthogonal Hademard-type matrix reflecting the testing conditions, and [beta]i are the unknown parameters. There are n0 testing positions available, each one during the time interval [0,t0]. This interval is divided into k stages of length ti, I = 1, ... , k, and on each of these stages all devices operate under a fixed testing regime. Each device which fails is immediately restored and continues to operate. A closed maximum likelihood solution is given for estimates of [beta]i. An expression for [Sigma]AsVar[[beta]i] is derived, which serves for obtaining an approximate optimal duration of the ith testing stage, ti*. It is shown that ti* is proportional to the square root of the mean lifetime for the corresponding testing regime.