Calculation of small-sample weibull tolerance bounds for accelerated testing

In this paper it is assumed that in the range of interest the Arrhenius model or the inverse power law, or more generally, some known polynomial function relates a specified function of level of stress and the logarithm of time-to-failure. The number of stress levels at which testing is performed is assumed to be at least one more than the degree of the polynomial, and the distribution of time-to-failure at these stress levels and at the nominal level is assumed to be two-parameter Weibull with equal shape parameter and scale parameter varying with stress level. The numbers of tests made at the various stress levels need not be equal, but more than a single test must be made at one or more levels. Testing may be censored, even progressively censored, in some cases,For this model, a simple procedure is developed for calculating approximate small-sample lower tolerance bounds (confidence bounds for distribution percentiles) corresponding to the nominal stress level These calculations can be made at the same time point estimates are made of nominal-level percentiles. Numerical comparisons with exact (Monte Carlo generated) tolerance bounds are tabulated