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Volume 14
Issue 9
10.3390/axioms14090653
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches

by
Hadiqa Basit
1,
Mahmoud M. Abdelwahab
2,
Shakila Bashir
1,*,
Aamir Sanaullah
3,*,
Mohamed A. Abdelkawy
2 and
Mustafa M. Hasaballah
4,*
1
Department of Statistics, Forman Christian College (A Charted University), Lahore 54600, Pakistan
2
Department of Mathematics and Statistics, Faculty of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
3
Department of Statistics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan
4
Department of Basic Sciences, Marg Higher Institute of Engineering and Modern Technology, Cairo 11721, Egypt
*
Authors to whom correspondence should be addressed.
Axioms 2025, 14(9), 653; https://doi.org/10.3390/axioms14090653
Submission received: 30 June 2025 / Revised: 9 August 2025 / Accepted: 17 August 2025 / Published: 22 August 2025
(This article belongs to the Special Issue Methods and Applications of Advanced Statistical Analysis, 2nd Edition)
Versions Notes

Abstract

Industrial systems often rely on specialized redundant systems to enhance reliability and prevent unexpected failures. This study introduces a novel three-parameter model, the Poisson–Weibull distribution (PWD), and discovers its various key properties. The primary focus of the study is to develop stress–strength (SS) model based on this newly developed distribution. Parameter estimation for both the PWD and SS models is carried out using maximum likelihood estimation (MLE) and Bayesian estimation techniques. Given the complexity of the proposed distribution, numerical approximation techniques are employed to obtain reliable parameter estimates. A comprehensive simulation study employing the Monte Carlo simulation (MCS) and Markov Chain Monte Carlo (MCMC) examines the behavior of the PWD and SS model parameters under various scenarios. The development of the SS model enhances understanding of the PWD’s dynamics while providing practical insights into its real-life applications and limitations. The effectiveness of the proposed distribution and the SS reliability measure is established through applications to real-life data sets.
Keywords: stress-strength model; Monte Carlo simulation; Bayesian estimation; Weibull distribution; reliability analysis stress-strength model; Monte Carlo simulation; Bayesian estimation; Weibull distribution; reliability analysis

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MDPI and ACS Style

Basit, H.; Abdelwahab, M.M.; Bashir, S.; Sanaullah, A.; Abdelkawy, M.A.; Hasaballah, M.M. A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches. Axioms 2025, 14, 653. https://doi.org/10.3390/axioms14090653

AMA Style

Basit H, Abdelwahab MM, Bashir S, Sanaullah A, Abdelkawy MA, Hasaballah MM. A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches. Axioms. 2025; 14(9):653. https://doi.org/10.3390/axioms14090653

Chicago/Turabian Style

Basit, Hadiqa, Mahmoud M. Abdelwahab, Shakila Bashir, Aamir Sanaullah, Mohamed A. Abdelkawy, and Mustafa M. Hasaballah. 2025. "A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches" Axioms 14, no. 9: 653. https://doi.org/10.3390/axioms14090653

APA Style

Basit, H., Abdelwahab, M. M., Bashir, S., Sanaullah, A., Abdelkawy, M. A., & Hasaballah, M. M. (2025). A Novel Poisson–Weibull Model for Stress–Strength Reliability Analysis in Industrial Systems: Bayesian and Classical Approaches. Axioms, 14(9), 653. https://doi.org/10.3390/axioms14090653

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