Statistical Inference of Stress-Strength Reliability for the Exponential Power (EP) Distribution Based on Progressive Type-II Censored Samples

Abstract

Suppose that X represents the stress which is applied to a component and Y is strength of this component. Let X and Y have Exponential Power (EP) distribution with $(\alpha_1,\beta_1)$ and $(\alpha_2,\beta_2)$ parameters, respectively. In this case, stress-strength reliability (SSR) is shown by $P=P(X<Y)$. In this study, the SSR for EP distribution are obtained with numerical methods. Also maximum likelihood estimate (MLE) and approximate bayes estimates by using Lindley approximation method under squared-error loss function for SSR under progressive type-II censoring are obtained. Moreover, performances of these estimators are compared in terms of MSEs by using Monte Carlo simulation. Furthermore coverage probabilities of parametric bootstrap estimates are computed. Finally, real data analysis is presented.