General model for variable-stress accelerated life testing

Accelerated tests using a time-varying stress application have been used to assure failures quickly. This is highly desirable given the pressure on industry today to shorten new product introduction time. The most basic and useful type of time-varying stress test is a step-stress test. Step stress testing is a special kind of accelerated life testing (ALT) in which the stress on each specimen is increased step-by-step over time; it can substantially shorten the reliability test's duration. This paper presents a general theoretical model capable of modeling results ranging from the commonly used simple step-stress testing which is extensively investigated in the literature to more complex step-stress testing which have not been investigated by others. We first develop a general step stress accelerated life testing (SSALT) model based on the accelerated factors. Utilizing the maximum likelihood estimation method, the likelihood function is formulated and solved for complete and suspended data and for the Weibull, exponential and Lognormal as the underlying life distributions. The Arrhenius, Eyring, Inverse Power Law, Temperature-Humidity, and Temperature-Non Humidity models can be assumed for the life-stress relationship. Confidence bounds on the estimates are quantified using the variance-covariance matrix. Secondly, we discuss the relationship between the proposed model and the previous models; it can also be shown that the most widely used SSALT models like Nelson's Cumulative Damage Model, Gouno (2001)'s model, Xiong and Milliken (2002)'s model are the subsets of the proposed model. Finally, we demonstrate how to apply the proposed SSALT model to engineering field, and illustrate the application of the model studied in this paper to a real data. This research is novel in that a theoretical generalized model for accelerated life testing is developed and then verified experimentally with laboratory data. The results of our experiment demonstrate that the proposed model is a promising SSALT model with the potential of becoming very useful in practice and of leading to further generalization of component and product reliability estimations. Therefore, it provides a convenient way to interpret the SSALT results and a new viewpoint on how to optimally design SSALT plans.