Expectation Maximization Algorithm for One Shot Device Accelerated Life Testing with Weibull Lifetimes, and Variable Parameters over Stress

In reliability analysis, accelerated life-tests are commonly used for inducing more failures, thus obtaining more lifetime information in a relatively short period of time. In this paper, we study binary response data collected from an accelerated life-test arising from one-shot device testing based on a Weibull lifetime distribution with both scale and shape parameters varying over stress factors. Log-linear link functions are used to connect both scale and shape parameters in the Weibull model with the stress factors. Because no failure times of units are observed, we use the EM algorithm for computing the maximum likelihood estimates (MLEs) of the model parameters. Moreover, we develop inferences on the reliability at a specific time, and the mean lifetime at normal operating conditions. This method of estimation is then compared with Fisher scoring and least-squares methods in terms of mean square error as well as tolerance value, computational time, and number of cases of divergence. The asymptotic confidence intervals and parametric bootstrap confidence intervals are also developed for some parameters of interest. A transformation approach is also proposed for constructing confidence intervals. A simulation study is then carried out to demonstrate that the proposed estimators perform very well for data of the considered form. Such accelerated one-shot device testing data can also be found in survival analysis. For an illustration, we consider here an application of the proposed algorithm to mice tumor toxicology data from a study involving the development of tumors with respect to risk factors such as sex, strain of offspring, and dose effects.