Stress-Strength Reliability of Two-Parameter Exponential Distribution Based on Progressively Type-II Censored Data

Abstract

Introduction: Stress-strength models has achieved considerable attention in recent years due to its applicability in various areas like engineering, quality control, biology, genetics, medicine etc. This paper investigates estimation of the stress-strength reliability parameter  in two-parameter exponential distributions under progressively type-II censored samples.
Methods: The maximum likelihood and the best linear unbiased estimates of  are obtained, and the Bayes estimates of  are computed under the squared error, linear-exponential, and Stein loss functions. Also, confidence intervals of stress-strength reliability such as the bootstrap confidence intervals, highest posterior density credible interval, and confidence interval based on the generalized pivotal quantity are obtained. Results: Using a simulation study, the point estimators and confidence intervals are evaluated and compared. A set of real data is presented for better clarification of the issue.
Conclusion: The results demonstrated that with increasing the sample size, in almost cases the estimated
risk of all the estimators decrease. Also, in almost all cases the Bayes estimator under the linear-exponential
loss function has smaller estimated risk than the other estimators. Based on our simulation, the expected
lengths of all intervals tend to decrease when the sample size increases. Moreover, the highest posterior density confidence intervals are shorter than the others intervals for all the values of P(Y<X).