Multi-scenario reliability stress-strength models based on Topp-Leone and generalized Rayleigh distributions

Al-Rikabi, Karrar Mohammed Obaid; Heydari, Ali Akbar; Khamnei, Hossein Jabbari

doi:10.47974/JSMS-1360

Open Access Research Article

Multi-scenario reliability stress-strength models based on Topp-Leone and generalized Rayleigh distributions

^*Karrar Mohammed Obaid Al-RikabiCorresponding authorm.karrar@tabrizu.ac.irDepartment of Statistics Faculty of Mathematics, Statistics, and Computer Science University of Tabriz Tabriz, IranView full profile → , Ali Akbar Heydariheydari@tabrizu.ac.irDepartment of Statistics Faculty of Mathematics, Statistics, and Computer Science University of Tabriz Tabriz, IranView full profile → , Hossein Jabbari Khamneihjabbari@tabrizu.ac.irDepartment of Statistics Faculty of Mathematics, Statistics, and Computer Science University of Tabriz Tabriz, IranView full profile →

* Corresponding author · click or hover a name for details

pp. 1037–1048Vol. 28Issue 6September 2025DOI: 10.47974/JSMS-1360XML

Received:: 09 Jul 2024
Published Online:: 09 Sep 2025
Article type:: Research Article
Language:: EN
Article no.:: JSMS-1360
Pages:: 1037–1048

Abstract

This paper examines the role of reliability theory in system analysis, focusing on system representation, quantification, and uncertainty modeling. It explores various multi-scenario reliability stress-strength models based on Topp-Leone and Generalized Rayleigh distributions, covering environments with multiple stresses, strength variability, and constrained stress conditions. The study addresses modeling complexity in stress-strength relationships for multi-component, n-standby, and cascade systems. Several parameter estimation methods are evaluated, including maximum likelihood estimation, the Jackknife, and Bayesian estimators, with a Monte Carlo simulation used to compare their performance. The results indicate that maximum likelihood estimation and Jackknife methods are superior due to their low bias and Mean Squared Error across various scenarios and sample sizes, demonstrating robustness and reliability. Bayesian methods offer flexibility but require careful management of priors and data volume, while non-parametric methods tend to have higher bias and MSE, particularly in complex scenarios or with smaller sample sizes.

Keywords

Reliability theory Stress-strength models Topp-Leone distribution Generalized rayleigh distribution Multi-stress environments Adaptability Constrained stress Multi-component systems n-standby systems Cascade systems

Subject Classifications

90B25

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