Observational analysis demonstrated that fuzzy methods improved reliability estimates in lifetime data, indicating the Bayes method may outperform traditional approaches.
The study has examined the estimation of Frechet distribution parameters with the shape parameter (α) and the scale parameter (β). Two estimation methods are used based on the maximum likelihood and Bayes methods. The life time data are fuzzy numbers. These estimations of parameters are employed to estimate the fuzzy reliability function of the distribution and to select the best estimate of the fuzzy reliability function by comparing the mean squares error (MSE) and the average absolute proportional error (MAPE). The results of simulation showed that the fuzziness is better than the real for all sample sizes and the fuzzy reliability at the estimates of the Bayes estimated is better than the maximum likelihood method. It gives the lowest average MSE and MAPE until to arrive at a minimum at sample size of n = 500.
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Neamah et al. (2020) studied this question.
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