Optimal design of accelerated life tests under modified stress loading method

Abstract

Accelerated life tests(ALTs) have been effectively used to quickly obtain information on the lifetimes of highly reliable products. Most previous works on determining optimal ALT plans assume instantaneous changes in stress levels, which may not be possible or desirable in practice due to the limited capability of equipment, or due to possible stress shocks or any other undesirable failure modes. In this thesis, we consider the case where a change in stress level is made at a finite rate, and develop two types of ALT plans assuming exponential lifetimes of test units. One is the modified step-stress ALT plan, and the other is modified constant-stress ALT plan. Then, these two plans are compared in terms of the asymptotic variance of the maximum likelihood estimator of the log mean lifetime at the use condition. Computational results indicate that for both types of plans the asymptotic variance is not sensitive to the stress increasing rate R if R is sufficiently large. This implies that the proposed stress loading method can be utilized to avoid potential stress shocks with little loss of the asymptotic variance. In addition, the modified step-stress ALT generally performs better than the constant-stress ALT in terms of the asymptotic variance unless R and the probability of failure at the use condition are small.