Fuzzy stress and strength reliability based on the generalized mixture exponential distribution

Abstract

In this paper, we will discuss the stress and strength reliability and the fuzzy stress and strength reliability based on the generalized mixtures of exponential distribution. A fuzzy membership function is defined as a function of the difference between stress and strength values and is increasing whenever X > Y. Several estimation methods, such as Maximize likelihood estimation method, Weighted Least squared estimation method and Percentile estimation method, will be provided to estimate the corresponding measures. Simulation studies are constructed to compare the performances of the proposed estimators. The comparisons are based on the biases, mean squared errors (MSEs) and the efficiency of the estimators. One data analysis has been performed for illustrative purpose.