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In this paper, we consider the situation under a life test, in which thefailure time of the test units are not related deterministically to anobservable stochastic time varying covariate. In such a case, the jointdistribution of failure time and a marker value would be useful for modelingthe step stress life test. The problem of accelerating such an experiment isconsidered as the main aim of this paper. We present a step stress acceleratedmodel based on a bivariate Wiener process with one component as the latent(unobservable) degradation process, which determines the failure times and theother as a marker process, the degradation values of which are recorded attimes of failure. Parametric inference based on the proposed model is discussedand the optimization procedure for obtaining the optimal time for changing thestress level is presented. The optimization criterion is to minimize theapproximate variance of the maximum likelihood estimator of a percentile of theproducts' lifetime distribution.

Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model