Constant Stress Accelerated Life Test: Different Methods of Estimation Under the Exponentiated Power Lindley Distribution

Accelerated life testing has been used frequently in several fields as it provides an economical way for obtaining failure time data rapidly or in a shorter time as compared to normal operating conditions. The lifetime data of a product at a constant stress level are assumed to have an exponentiated power Lindley distribution, and the model's shape parameter should have a log-linear relationship with the stress level. Statistical inference on the estimation of the underlying model parameters as well as the reliability function under usual conditions are estimated based on nine frequentist methods of estimation, namely, method of maximum likelihood, method of least square and weighted least square, method of maximum product of spacing, method of minimum spacing absolute distance, method of minimum spacing absolute-log distance, method of Cramer-von Mises, method of Anderson-Darling and right-tail Anderson-Darling. A Monte Carlo simulation study has been carried out to compare the performance of the proposed methods of estimation in terms of mean relative estimate, and mean squared error using small and large sample sizes. As an illustration, one accelerated life test data set is considered to obtain bootstrap confidence intervals for the unknown parameters, predicted shape parameter, predicted reliability function and the mean time to failure (MTTF) at different stress levels and to see how the model and the proposed methods works in practice for the dataset.