Estimation of Stress-Strength Reliability Following Extended Chen Distribution

Abstract

This paper considers the estimation of the stress-strength parameter [Formula: see text] under progressive type-II censored samples, where [Formula: see text] is the strength and [Formula: see text] is the stress follow extended Chen distribution. It is assumed that [Formula: see text] and [Formula: see text] are independent. Two cases are studied. The uniformly minimum variance unbiased estimator is derived when a common scale parameter and a common shape parameter are known. In both the cases, the maximum likelihood estimates are computed using numerical iteration technique. Sufficient conditions are derived under which the MLEs of [Formula: see text] exist and unique. The Bayes estimates with respect to the squared error loss function are evaluated using Lindley’s and MCMC methods. Interval estimates are also constructed using asymptotic and bootstrap techniques. A simulation study is carried out to compare the proposed methods. Finally, data analysis has been performed on two real-life data sets for the purpose of illustration.