Estimation of Fuzzy Reliability Function Employed Bayes Method With Practical Application

Abstract

In this research we will treat fuzzy lifetime data that each value does not have minimum and maximum limitation which enable us to appoint the suitable belonging degrees but all lifetime data have minimum restriction which represent the beginning life time, and maximum one that represents the end of lifetime, This paper discussed two procedures to estimate the fuzzy reliability, Bayes procedure that includes the following :1-Sample data are fuzzy and the prior distribution for parameter includes an un fuzzy parameter.2- Sample data are fuzzy and the prior distribution for parameter includes a fuzzy parameter. Employed the Rayleigh distribution form for sample data, and Gama distribution for the prier distribution for the parameter of Rayleigh distribution parameter in the data taken from the Nujaiba power station of the Ministry of Electricity and for two different values (2.1) for the primary distribution parameters of Gamma distribution, From the results obtained in the applied side, it was found that the first case of the Bayes method for α values (0.001,0.002,0.003) is relatively better than the other cases of the Bayes method in estimating the fuzzy reliability, and at α values (0.004,0.005,0.006, 0.007,0.008,0.009,0.01) The third case of the Bayes method is best than the other cases of the Bayes method in estimating the fuzzy reliability when the fuzzy sample data have membership degree a lower or equal to 0.001.