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 timetof an item subjected to levelxof 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 andhare nonnegative nondecreasing functions ofxandt, respectively;Fis 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.