Optimal Plans and Estimation of Constant-Stress Accelerated Life Tests for the Extension of the Exponential Distribution under Type-I Censoring

Accelerated life tests (ALTs) are usually applied for life testing of devices that are extremely reliable. In this article, a constant-stress ALT is considered when the lifetime of a test unit has an extension of the exponential distribution. It can be accepted as an alternate to Weibull, gamma, and exponentiated exponential distributions. The scale parameter of lifetime distribution is supposed to be a log-linear function of the stress levels. The maximum likelihood estimates of the parameters, as well as Fisher information matrix, are derived. In addition, Bayes estimates of the model parameters are obtained. The optimal proportion of test units allocated to every stress level is derived depending on D-, C-, and A-optimality criteria. Moreover, two real data examples are analyzed to explain the importance of the extension of the exponential distribution in reliability studies. Thereafter, a Monte Carlo simulation study is carried out to check the efficacy of the estimation techniques and the optimality criteria.