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

Author

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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)

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 .

Suggested Citation

  • Weizhong Tian & Chengliang Tian & Sha Li & Yunchu Zhang & Jiayi Han, 2024. "Fuzzy Stress and Strength Reliability Based on the Generalized Mixture Exponential Distribution," Mathematics, MDPI, vol. 12(17), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:17:p:2684-:d:1466499
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    References listed on IDEAS

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    1. Ali Akbar Jafari & Saeede Bafekri, 2021. "Inference on stress-strength reliability for the two-parameter exponential distribution based on generalized order statistics," Mathematical Population Studies, Taylor & Francis Journals, vol. 28(4), pages 201-227, October.
    2. Yang Liu & Majid Khan & Syed Masroor Anwar & Zahid Rasheed & Navid Feroze & Sanku Dey, 2022. "Stress-Strength Reliability and Randomly Censored Model of Two-Parameter Power Function Distribution," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-12, June.
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