Planning accelerated life tests with three constant stress levels

This paper presents two alternative ways of planning for constant stress accelerated tests (CSALT) with three stress levels that not only optimize the stress levels but also optimize the sample allocations. In the first method, we consider limiting the chances of inconsistency arising from non-parallel lines when data from different stress levels are plotted on the same probability plot. For the second method, we consider minimizing both the variance of some estimate and the influence arising from the addition of middle stress when the assumed stress–life relation is true. The test plan generated using the first approach is useful when one needs to establish beyond reasonable doubt that the shape parameters of the assumed Weibull distributions (or other parameters that are related to the slope of the probability plot for other distributions) at different stress levels are different. The second approach is useful when one needs to validate a particular stress–life relationship. Both approaches are formulated as constrained non-linear programs.