Estimation of the fuzzy reliability function using two-parameter exponential distribution as prior distribution

In this research, the fuzzy reliability function of the series system has been estimated using Bayes approach and Mellin transformation. It is based on the existence of two parameter exponential distribution as a previous distribution with the existence of a similar quadratic loss function, square loss function and non- asymmetric precautionary loss function. To apply the Bayes approach, the distribution parameters are assumed to be "random variables", and the traditional Bayes approach was used to obtain Bayes fuzzy capabilities by using Resolution Identity Theory in the fuzzy set. The simulation approach has been applied in this study to know the effect of α value on the fuzzy reliability function capabilities. The experiment has been carried out by assuming different values of the parameters as well as the sizes of the different samples. Furthermore, the applied part has dealt with the fuzzy reliability function estimation of both the quadratic loss function and the precautionary loss function with different α values using nonlinear membership functions. Some mathematical equations have been used to calculate the membership scores of the Bayes estimated points. This purpose has been achieved by converting the original problem into a non-linear programming problem and then divided it into eight secondary problems. The results have been obtained using the LINGO and GAMS programs