Design of accelerated tests under varying stress

Abstract

This thesis considers the problem of optimally designing accelerated tests (ATs) under varying stress. First, two types of accelerated life test (ALT) plans are developed assuming that the stress is increased at some finite rate to avoid potential stress shocks or due to the inherent capability of equipment. One is the modified step-stress ALT plan, and the other is the modified constant-stress ALT plan. For both cases, exponential lifetimes of test units and type I censoring are assumed. These two ALT plans are compared in terms of the asymptotic variance of the maximum likelihood estimator (MLE) of the log mean lifetime at the use condition (i.e. $avar[ln \hat theta(0)]$). Computational results indicate that, for both types of plans, $avar[ln \hat theta(0)]$ is not sensitive to the stress-increasing rate $R$, if $R$ is greater than or equal to 10, say, in the standardized scale. This implies that the proposed stress loading method can be used effectively with little loss in statistical efficiency. In terms of $avar[ln \hat theta(0)]$, the modified step-stress ALT generally performs better than the modified constant-stress ALT, unless $R$ or the probability of failure until the censoring time under a certain stress-increasing rate is small. The progressive-stress ALT plan is also compared with the above two modified ALT plans in terms of $avar[ln \hat theta(0)]$, using the optimal stress-increasing rate $R^*$ determined for the former. It is found that the proposed ALT performs better than the progressive-stress ALT for the parameter values considered. Furthermore, sensitivities of the proposed plans to mis-specifications of failure probabilities are also assessed. Secondly, optimal step-stress accelerated degradation test (step-ADT) and progressive-stress accelerated degradation test (progressive-ADT) plans are developed under the assumptions of destructive testing, a simple constant rate relationship between the stress and the performance of a unit, and a c...