Multicomponent Stress-Strength Reliability estimation based on Unit Generalized Exponential Distribution

Estimation of stress-strength reliability is considered based on frequentist and Bayesian methods of estimation when both stress and strength variables follow unit generalized exponential distributions. In frequentist method we consider maximum likelihood, least squares, weighted least squares and maximum product spacing methods to estimate system reliability when a common scale parameter is unknown. Further asymptotic and bootstrap intervals of system reliability are obtained. Next, we discuss Bayesian procedure under different loss functions using gamma and weighted Lindley priors for model parameters to estimate system reliability. Subsequently, highest posterior density credible intervals are also obtained. Besides, uniformly minimum variance unbiased estimator of system reliability is obtained when the common scale parameter is known. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of proposed estimates with respect to various criteria. Finally, to show the applicability of the proposed methodologies in a real-life scenario, an engineering data set is analyzed. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-ncnd/4.0/).

Automated summary

This paper considers the estimation of stress-strength reliability using both frequentist and Bayesian methods when both stress and strength variables follow unit generalized exponential distributions. The frequentist methods include maximum likelihood, least squares, weighted least squares, and maximum product spacing methods. The Bayesian methods use gamma and weighted Lindley priors for model parameters. Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates, and an engineering dataset is analyzed to demonstrate the applicability of the methods.