Accelerated Degradation Test Planning Using the Inverse Gaussian Process

The IG process models have been shown to be an important family in degradation analysis. In this paper, we are interested in optimal constant-stress accelerated degradation tests (ADTs) planning when the underlying degradation follows the inverse Gaussian (IG) process. We first consider ADT planning for the IG process without random effects. Asymptotic variance of the estimate of a lower quantile is derived, and the objective of the planning is to minimize this variance by properly choosing the testing stresses, and the number of samples allocated to each stress. Next, ADT planning for a random-effects IG process model is considered. We then applied the IG process to fit the stress relaxation data of a component, and use the developed methods to help with the optimal ADT design.