Bayes Estimator for Fuzzy Reliability Based on Pareto Distribution and Degroot Loss Function

Abstract

This paper deals with the estimation of the reliability function with a fuzzy environment. The Bayesian method was used to get the fuzzy Bayes estimation based on Pareto distribution for data. The prior distribution of the parameter is the Gamma distribution and used asymmetric loss function which is the Degroot loss function. The sample distribution parameters are considered to be fuzzy and prior distribution parameters are non-fuzzy. The researchers found by using simulation the estimated value and the MSE value of the fuzzy reliability function decrease by increasing the value of the degree of membership and by increasing the sample size.