Nonparametric Analyses for Two-Level Single-Stress Accelerated Life Tests

In accelerated life testing, information is sought about a process at normal stress levels by studying it at higher stress levels. Let Pr(t; x) be the probability of failure by time t of an item subjected to level x of a stress. In this article, I consider the nonparametric proportional hazards model. Pr(t; x) = 1 – e −g(x)h(t), and the nonparametric accelerated failure time model, Pr(f; x) = F(g(x)t), where g and h are nonnegative nondecreasing functions of x and t, respectively; F is an arbitrary distribution function; and g has sigmoid (S-shaped) curvature. I develop confidence bounds for low-stress long-time probabilities and quantiles. I also discuss a goodness-of-fit test of the proportional hazards model. The results, which are primarily for data at two levels of stress, accommodate simple right censoring.