Fuzzy Stress and Strength Reliability Based on the Generalized Mixture Exponential Distribution

This paper discusses the reliability of stress and strength,R, and fuzzy stress and strength reliability, RF, based on generalized mixtures of exponential distributions. We propose several estimation methods, such as the maximize likelihood estimation, the weighted least-squares estimation, and the percentile estimation, to estimate the corresponding measures. Simulation studies have been conducted to compare the proposed estimators’ performance using different settings. These comparisons are based on biases (Bias) and mean squared errors (MSEs), and we find that MSE(PE)>MSE(MLE)>MSE(WLE) and |Bias(PE)|>|Bias(WLE)|>|Bias(MLE)| in most cases. Moreover, the values of RF have the same pattern as R, and the values of MSEs and biases for RF are smaller than R. As the sample size increases, the values of biases for both reliabilities decrease and approach 0. Ultimately, we apply the proposed methods to a data set to illustrate its significance. We find that the estimated values of R are greater than those of RF for all the estimation methods. Moreover, the fuzzy estimators of RF are approximately equal to the estimators R.