Design of accelerated degradation tests based on stochastic process models

Abstract

As components or products become more reliable, it is getting more difficult to obtain reliability-related informations within an affordable amount of time. An accelerated degradation test (ADT) is a useful tool which has been employed in industry to overcome such difficulties. In an ADT, it is important that the design of the ADT be carefully thought out beforehand with the aim of obtaining the most precise and efficient estimates possible of the quantities of interest. In this thesis, we develop optimal ADT plans assuming that the degradation characteristic follows either a Wiener or a gamma process model. For the former case, optimal ADT plans with a single or two stress variables are developed under constant-stress loading (Chapters III and IV), while for the latter case, a single stress variable is considered (Chapter V). Unlike the previous works on planning ADTs based on stochastic process models, the test stress levels and the proportion of test units allocated to each stress level are determined such that the asymptotic variance of the maximum likelihood estimator (MLE) of the $\It{q}-th quantile of the lifetime distribution at the use condition is minimized, and the sample size is determined under the constraint on the precision of the estimator of the $\It{q}-th quantile of the lifetime distribution at the use condition. In addition, compromise plans with a single stress variable are also developed to provide means to check the validity of the acceleration model in Chapters III and V. Finally, using an example, sensitivity analysis procedures are presented for evaluating the robustness of optimal and compromise plans against the uncertainty in the pre-estimated parameter value, and especially in Chapter III, the importance of optimally determining test stress levels and the proportion of units allocated to each stress level are illustrated.