Accelerated life testing (ALT) has been widely applied to many industries as an answer to the need of testing highly reliable products with long-term performance. Recently, step-stress accelerated life testing (SSALT) has been used in place of the constant stress ALT in order to further accelerate the failure process and to explore potential failure modes. The statistical inference procedure for SSALT models has not been thoroughly discussed so far. This study focuses on developing the maximum likelihood method and Bayesian approach to the model estimation based on the special data structure of the SSALT data with exponential failure time distribution. The improvement on the statistical precision of estimator and the reduction of required sample size are discussed.

This study consists of three main research contributions. First, a general Bayesian inference procedure is presented for a simple SSALT with type-II censoring and it is extended to a general SSALT containing multiple stress levels. For the Bayesian analysis the prior distribution of the parameters of life-stress function is formulated and the joint posterior distribution is derived via the Bayes conjugacy. Second, the statistical inference of exponential SSALT model is developed by utilizing techniques of generalized linear models (GLMs). For this GLM SSALT model, both maximum likelihood estimation and the Bayesian approach are discussed. The iterative weighted least square (IWLS) method is used for ML estimation, and Jeffreys' noninformative prior and the Markov chain Monte Carlo technique are applied for Bayesian estimation. Third, the GLM approach is extended to the Weibull SSALT model with interval censoring. Through a 2-stage iterative method and bootstrapping, the estimation procedure is implemented. The GLM technique provides a significant flexibility for the choice of computational tools. Numerical examples using industrial data are presented for the validation and illustration of the proposed method.