Fuzzy System Reliability Analysis for Kumaraswamy Distribution: Bayesian and Non-Bayesian Estimation with Simulation and an Application on Cancer Data Set

Abstract

This paper proposes the fuzzy Bayesian (FB) estimation to get the best estimate of the unknown parameters of a two-parameter Kumaraswamy distribution from a frequentist point of view. These estimations of parameters are employed to estimate the fuzzy reliability function of the Kumaraswamy distribution and to select the best estimate of the parameters and fuzzy reliability function. To achieve this goal we investigate the efficiency of seven classical estimators and compare them with FB proposed estimation. Monte Carlo simulations and cancer data set applications are performed to compare the performances of the estimators for both small and large samples. Tierney and Kadane approximation is used to obtain FB estimates of traditional and fuzzy reliability for the Kumaraswamy distribution. The results showed that the fuzziness is better than the reality for all sample sizes and the fuzzy reliability at the estimates of the FB proposed estimated is better than other estimators, it gives the lowest Bias and root mean squared error.