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 (α1, β1) and (α2, β2) 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.

The power-linear hazard rate distribution and estimation of its parameters under progressively type-II censoring

“…Note that, if R1 = R2 = ... = Rm = 0, the progressive censoring scheme is reduced to complete sampling scheme and if R1 = R2 = ... = Rm−1 = 0 and Rm = n − m, this scheme reduces to conventional type-II censoring scheme. Statistical inference on the parameters of some distributions under progressive type-II censoring has been investigated by several authors such as Kus and Kaya [14], Jiang et al [12], Rastogi and Tripathi [26] and Akdam et al [1].…”

A new lifetime distribution: transmuted exponential power distribution

“…Many authors have focused on EP distribution recently. Some of these studies can be listed as follows; Chen [8], Barriga et al [7], Akdam et al [1]. The main purpose of this study is to suggest a new lifetime distribution as an alternative EP distribution by using QRTM.…”

Estimation of stress–strength reliability in the inverse Gaussian distribution under progressively type II censored data

“…In another study carried out by Shoaee and Khorram [43], the estimation of the stress-strength reliability R = P(Y < X) was considered based on progressively type II censored samples when X and Y were two independent twoparameter bathtub-shaped lifetime distributions. Besides, Akdam et al [3] obtained the estimation of R in the exponential power distributions based on censored data.…”