Analyzing ALT Data with Time-varying Stress Profile

We are interested in analyzing the accelerated life testing data obtained under time-varying stresses. This is a generalization of step-stress accelerated life test, where the stress levels are kept constant at each step. Our study shows that the time-dependent proportional hazard model, commonly appeared in the survival data analysis literature, is not applicable for ALTs, because this approach does not take accounts of the cumulative damage that the stress profile exerts on test units. Instead, we assume that products possess constant failure rates over small time intervals, and the change of failure rate by the stress variable still have the proportional hazard property. With these assumptions, it is possible to formulate the data according to a generalized linear model and statistical inferences on model parameters can be carried out. We demonstrate our models and inference procedures by using both synthetic and real datasets.