Stress-Strength Reliability for P(T<X<Z) using The New Weibull-Pareto Distribution

Abstract

In this paper, the reliability formula of the stress-strength model is derived for probability  of a component having strength X falling between two stresses T and Z, based on The New Weibull-Pareto Distribution with unknown parameter  and known and common parameters  and . Four methods for estimating the The New Weibull-Pareto parameters are discussed which are the Maximum Likelihood, Method of Moment, Least Square Method and Weighted Least Square Method, and the comparison between these estimations based on a simulation study by the mean square error criteria for each of the small, medium and large samples. The most important conclusion is that this comparison confirms that the performance of the maximum likelihood estimator works better for all experiments studied.