Bayesian Estimation of Stress-Strength P(T < X < Z) for Dagum Distribution

Abstract

In this paper, the reliability formula is derived for the stress-strength model of the probability P(T < X < Z) for a component’s strength X falling between two stresses T and Z, based on Dagum Distribution with unknown parameter β and known and common parameters λ and δ. Bayesian estimation is discussed to estimate the reliability under complete data by using Gamma prior based on two loss function (weighted and quadratic loss functions), and the comparison between these estimators based on a simulation study using mean square error criteria (MSE) for each of the small, medium and large samples. The most important conclusion is that this comparison confirms that the performance of the estimator according to the weighted loss function works better for the most experiments studied.