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

Weizhong Tian (), Chengliang Tian (), Sha Li, Yunchu Zhang and Jiayi Han
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Weizhong Tian: College of Big Data and Internet, Shenzhen Technology University, Shenzhen 518118, China
Chengliang Tian: College of Computer Science and Technology, Qingdao University, Qingdao 266071, China
Sha Li: School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
Yunchu Zhang: College of New Materials and New Energies, Shenzhen Technology University, Shenzhen 518118, China
Jiayi Han: College of New Materials and New Energies, Shenzhen Technology University, Shenzhen 518118, China

Mathematics, 2024, vol. 12, issue 17, 1-15

Abstract: This paper discusses the reliability of stress and strength, R , and fuzzy stress and strength reliability, R F , 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 M S E ( P E ) > M S E ( M L E ) > M S E ( W L E ) and | B i a s ( P E ) | > | B i a s ( W L E ) | > | B i a s ( M L E ) | in most cases. Moreover, the values of R F have the same pattern as R , and the values of MSEs and biases for R F 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 R F for all the estimation methods. Moreover, the fuzzy estimators of R F are approximately equal to the estimators R .

Keywords: stress and strength reliability; fuzzy; generalized mixtures exponential distribution; MLE (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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