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

Rebeca Klamerick Lima, Felipe Sousa Quintino, Melquisadec Oliveira, Luan Carlos de Sena Monteiro Ozelim (), Tiago A. da Fonseca and Pushpa Narayan Rathie
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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

J, 2024, vol. 7, issue 4, 1-17

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.

Keywords: stress–strength reliability; multicomponent system; l -max stable laws; p -max stable laws (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2024
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