Accelerated degradation test is a useful approach to predict the product lifetime at the normal use stress level, especially for highly reliable products. Two kinds of the lifetime prediction based on Gamma processes were studied. One was to predict the lifetime of the population from accelerated degradation data, and the other was to predict the lifetime of an individual by taking the accelerated degradation data as prior information. For an extensive application, the Gamma process with a time transformation and random effects was considered. A novel contribution is that a deducing method for determining the relationships between the shape and scale parameters of Gamma processes and accelerated stresses was presented. When predicting the lifetime of an individual, Bayesian inference methods were adopted to improve the prediction accuracy, in which the conjugate prior distribution and the non-conjugate prior distribution of random parameters were studied. The conjugate prior distribution only considers the random effect of the scale parameter while the non-conjugate prior distribution considers the random effects of both the scale and shape parameter. The application and usefulness of the proposed method was demonstrated by the accelerated degradation data of carbon-film resistors

A reliability acceptance test is used to investigate the reliability of products delivered by producer before buyer accepts them. However, the traditional reliability acceptance test based on lifetime data, which is conducted under a comparative low stress level, is time consuming. It is an interesting and useful issue to study how to design an optimal accelerated-stress reliability acceptance test (ASRAT) to improve test efficiency. An inverse Gaussian process was applied to model degradation data of products. Acceleration factor constant principle was applied to derive the expression of acceleration factor for the inverse Gaussian degradation model, so the termination time of ASRAT was obtained through acceleration factor. The asymptotic variance of termination time was selected as an objective function to establish the optimization model of the ASRAT plan. The decision variables, including accelerated stress level, sample size, and the number of measurement were optimized by minimizing the asymptotic variance of termination time under a total cost constraint. Then, an automatic algorithm based on MATLAB procedure was developed to help efficiently design optimal ASRAT plans. Finally, the proposed method was used to design an optimal ASRAT plan for a type of electric connector. Sensitivity analysis indicates that the optimal ASRAT plan is robust to small bias of parameter estimation. Moreover, simulation tests were conducted to demonstrate the usefulness of ASRAT and investigate the impact of degradation model misspecification on designing an optimal ASRAT plan.