Reliability Estimation of Stress-Strength Model for Binomial Exponential 2 Distribution

In this paper, the reliability of a system is discussed when the strength of the system and the stress imposed on it are independent, non-identical binomial exponential 2 distributed random variables. Different methods for estimating the reliability are applied. The maximum likelihood (ML), Wilson-Hilferty (WH) normal-based approximation and Bayesian methods are used in the estimation procedure. Also, we propose confidence intervals of the stress-strength reliability based on the approximate method, Bayesian method and Bootstrap methods (Boot-p and Boot-t). Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations. Finally, analysis of a real data set is presented for illustrative purposes.