Classical methods of estimation on constant stress accelerated life tests under exponentiated Lindley distribution

Abstract

Accelerated life testing is adopted in several fields to obtain adequate failure time data of test units in a much shorter time than testing at normal operating conditions. The lifetime of a product at constant level of stress is assumed to have an exponentiated Lindley distribution. In this paper, besides maximum likelihood method, eight other frequentist methods of estimation, namely, method of least square estimation, method of weighted least square estimation, method of maximum product of spacing estimation, method of minimum spacing absolute distance estimation, method of minimum spacing absolute-log distance estimation, method of Cramér-von-Mises estimation, method of Anderson-Darling estimation and Right-tail Anderson-Darling estimation are considered to estimate the parameters of the exponentiated Lindley distribution under constant stress accelerated life testing. Moreover, shape parameter and the reliability function under usual conditions are estimated based on aforementioned methods of estimation. To evaluate the performance of the proposed methods, a simulation study is carried out. The performances of the estimators have been compared in terms of their mean squared error using small, medium and large sample sizes. As an illustration, the model and the proposed methods are applied to two accelerated life test data sets.

Keywords: Accelerated life testing; Cramér–von-Mises estimation method; exponentiated Lindley distribution; least squares method; maximum likelihood method; weighted least squares method.