Abstract
In this paper we present two nonparametric accelerated life testing models, namely the accelerated failure time/cumulative exposure (AFT/CE) and proportional hazards/tampered failure rate (PH/TFR) models, and develop methods for obtaining the confidence bounds for low-stress cumulative failure probabilities and reliability functions, based on data collected from a step-stress accelerated life test. The approach is nonparametric in the sense that most of the functions, especially the damage rate function, involved in these two models do not assume any specific forms, except they satisfy certain verifiable conditions. The obtained upper bounds for the cumulative failure probabilities and lower bounds for the reliability functions under these two models are estimatable from the test data. To provide formal procedures for verifying the conditions of the damage rate function and for testing the goodness-of-fit (GOF) of the proposed models, the traditional step-stress test is slightly modified to obtain necessary data for these purposes so that the proposed procedures can be carried out. We have complete procedures for the AFT/CE model; but only partial results are obtained for the PH/TFR model. Finally, a simulated numerical example is used to illustrate the proposed methods for the AFT/CE model.