Estimating the Generalized Exponential Distribution Parameters and the Acceleration Factor Under Constant-Stress Partially Accelerated Life Testing with Type-II Censoring

Accelerated life testing (ALT) and partially accelerated life testing (PALT) are frequently used in modern reliability engineering. ALT and PALT are run to obtain information on the life of the products and materials in a shorter time and at lower cost. The experimental units are subject to stress conditions that are more severe than those encountered in normal use condition to induce early failures. ALT or PALT can be carried out using constant, step, progressive, cyclic and random stress loadings. This paper considers the problem of estimating the generalized exponential (GE) distribution parameters and the acceleration factor under constant-stress PALT model. The main objective is to derive the maximum likelihood estimators (MLEs) of the parameters of the GE distribution and the acceleration factor when the data are type-II censored from constant-stress PALT. Also, the performance of the MLEs is investigated numerically for different sample sizes and different parameter values using the mean square error. In addition, the approximate confidence intervals of the model parameters are constructed. Moreover, the likelihood ratio bounds (LRB) method is used to obtain confidence bounds of the model parameters when the sample size is small. For illustration, a simulation study is conducted. It is observed that the simulation results support the theoretical findings.