The Estimation of Survival Function for Modified Weibull Extension Distribution Using Two-Symmetric Pentagonal Fuzzy Numbers with Simulation

Abstract

In this paper, the parameters of the Modified Weibull Extension Distribution are estimated using the maximum likelihood estimator method and the Monte Carlo method in the simulation procedure to generate many different sample sizes, with many different replicates of the sample sizes. Following that finding, the Survival function’s estimate. Then fuzzify the estimation of the parameters for the same different sample sizes with the same difference in replicated sample sizes that was obtained from the Monte Carlo method in the simulation procedure by the new proposed method of expanding the Confidence Interval of estimated parameters to nine fuzzy numbers. Then, transform all the fuzzy parameters to crisp parameters using the proposed ranking functions with (proposed Linear Two- Symmetric Pentagonal Fuzzy Numbers, and proposed Non Linear Two-Symmetric Pentagonal Fuzzy Numbers). Accordingly, finding the Survival function. The outcome of Survival functions before and after fuzzy work will be compared using mean square error.