Quasi bayesian estimation of stress strength model for the power function distribution

The reliability of a system is the probability that when operating under stated environmental conditions, the system will perform its intended function adequately. We consider the strength of the system X and the stress Y as random variables. The component fails at the instant that the stress applied to it exceeds the strength and the component will function satisfactorily whenever X>Y. The quasi-likelihood function was introduced by Wedderburn (1974), to be used for estimating the unknown parameters in generalized linear models. In Quasi-Bayesian Estimation to construct a posterior distribution the likelihood function could be replaced with the natural exponential of the quasi-likelihood function. This method reduces to the usual Bayesian estimation if the quasi-likelihood and the log-likelihood function are identical. In this paper, we obtain Quasi Bayesian estimates for the stress –strength reliability for the power function distribution. We illustrate the performance of the estimators using a simulation study.