Using Nonparametric Analysis to Estimate the Reliability Function for Weibull Distribution

Abstract

With a wide increasing in industry and increasing mechanical and electronic complexities, increased attention to the study of reliability and methods of estimations, including non-parametric methods. The paper aims to estimate the reliability of the complex system that contains a large number of components by non-parametric method from transitions probability matrix that is estimated using stochastic processes. We used clustering analysis to estimate the transitions probability matrix of the stochastic processes, which is a representation of the study complex system, then find the equilibrium distribution of the process and from it, we can calculate the reliability of the system.By using simulation, we generated a data to estimates reliability function via parametric methods (method of moments, maximum likelihood methods) and non-parametric methods (empirical method, non-parametric analyze), when comparison between these methods by using IMSE, shown the estimators of Weibull reliability function using non-parametric analyze better than another selected methods, in case of small samples.