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With today's high technology, some life tests result in no or very few failures by the end of test. In such cases, an approach is to do life test at higher-than-usual stress conditions in order to obtain failures quickly. This study discusses the point and interval estimations of parameters on the simple step-stress model in accelerated life testing with progressive type II censoring. An exponential failure time distribution with mean life that is a log-linear function of stress and a cumulative exposure model are considered. We derive the maximum likelihood estimators of the model parameters. Confidence intervals for the model parameters are established by using pivotal quantity and can be applied to any sample size. A numerical example is investigated to illustrate the proposed methods.

Availability is an important measure of performance of repairable system. The steady state system availability has special importance since it demonstrates the performance of a system after it has been operated for long. The statistical inference about the steady state availability are particularly useful for practitioners. Much work has been done in this regard. Most of these researches proposed certain pivotal quantities for constructing confidence intervals of the steady state availability. Assuming both the lifetime and repair time follow gamma distribution with known shape parameters and unknown scale parameters, we propose a pivotal quantity for making inferences, and further derive the likelihood ratio tests. Tables of critical values are given for the convenience of applying the two-sided likelihood ratio test. Confidence intervals are also obtained by converting the acceptance regions.

In this paper, we developed a method for constructing confidence intervals for the parameters of lifetime distributions based on progressively type II censored data. The method produces closed form expressions for the bounds of the confidence intervals for several special cases of parameters and lifetime distributions. Closed form approximations are derived for the intervals for the parameters of the location or scale families of distributions. The method is illustrated with several examples and analyses of real data sets are included to illustrate the application of the method.