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Multicomponent Stress–Strength Reliability with Extreme Value Distribution Margins: Its Theory and Application to Hydrological Data

Author

Listed:
  • Rebeca Klamerick Lima

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil)

  • Felipe Sousa Quintino

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil)

  • Melquisadec Oliveira

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil)

  • Luan Carlos de Sena Monteiro Ozelim

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasilia 70910-900, Brazil)

  • Tiago A. da Fonseca

    (Gama Engineering College, University of Brasilia, Brasilia 70910-900, Brazil)

  • Pushpa Narayan Rathie

    (Department of Statistics, University of Brasilia, Brasilia 70910-900, Brazil)

Abstract

This paper focuses on the estimation of multicomponent stress–strength models, an important concept in reliability analyses used to determine the probability that a system will function successfully under varying stress conditions. Understanding and accurately estimating these probabilities is essential in fields such as engineering and risk management, where the reliability of components under extreme conditions can have significant consequences. This is the case in applications where one seeks to model extreme hydrological events. Specifically, this study examines cases where the random variables X (representing strength) and Y (representing stress) follow extreme value distributions. New analytical expressions are derived for multicomponent stress–strength reliability (MSSR) when different classes of extreme distributions are considered, using the extreme value H -function. These results are applied to three l -max stable laws and six p -max stable laws, providing a robust theoretical framework for multicomponent stress–strength analyses under extreme conditions. To demonstrate the practical relevance of the proposed models, a real dataset is analyzed, focusing on the monthly water capacity of the Shasta Reservoir in California (USA) during August and December from 1980 to 2015. This application showcases the effectiveness of the derived expressions in modeling real-world data.

Suggested Citation

  • Rebeca Klamerick Lima & Felipe Sousa Quintino & Melquisadec Oliveira & Luan Carlos de Sena Monteiro Ozelim & Tiago A. da Fonseca & Pushpa Narayan Rathie, 2024. "Multicomponent Stress–Strength Reliability with Extreme Value Distribution Margins: Its Theory and Application to Hydrological Data," J, MDPI, vol. 7(4), pages 1-17, December.
    • Handle: RePEc:gam:jjopen:v:7:y:2024:i:4:p:32-545:d:1534450
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    References listed on IDEAS

    as
    1. Bucher, Axel & Segers, Johan, 2017. "On the maximum likelihood estimator for the Generalized Extreme-Value distribution," LIDAM Reprints ISBA 2017039, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Yuhlong Lio & Tzong-Ru Tsai & Liang Wang & Ignacio Pascual Cecilio Tejada, 2022. "Inferences of the Multicomponent Stress–Strength Reliability for Burr XII Distributions," Mathematics, MDPI, vol. 10(14), pages 1-28, July.
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