Bayesian Estimation of the Inverse Rayleigh Process under a Non-Homogeneous Poisson Process Framework

Section: Article
Issue
Vol. 22 No. 2 (2025): Volume 22 Issue 2
Published
Dec 1, 2025
Pages
163-175

Abstract

The rationale on which this study is based is that accurate and dependable means to obtain time-dependent failure rates in repairable systems, especially in cases that are not homogeneous, are required, and the conventional models are not always in a position to meet these demands. To address this, the research targets at use of Inverse Rayleigh Process (IRP) within a Non-Homogeneous Poisson Process (NHPP) paradigm, a model of the system failures that suits the use of the stochastic model of a system. To improve the accuracy of parameter estimation, the Maximum Likelihood Estimation (MLE) approximation and Bayesian methods are studied and here the solving of the analytical problems due to intractable posterior distributions when using Laplace approximations is sought. Zooming over the simulation experiments that have been conducted on various sample sizes, evaluated through Root Mean Square Error (RMSE), shows that the Bayesian estimator in particular Bayes II prior outperforms MLE. Lastly, the proposed approaches are confirmed on the real-life failure records in the Mosul Gas Power Plant, which confirms the effectiveness of the Bayesian approach in the modeling of the coupled reliability systems in practice and more precisely in the data-scarce context

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Author

Kawar Badie Mahmood

Department of Information Technology, Amedi Technical Institute, Duhok Polytechnic University, Iraq.

Identifiers

https://doi.org/10.33899/iqjoss.v22i2.54201
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How to Cite

Mahmood, K. B. . (2025). Bayesian Estimation of the Inverse Rayleigh Process under a Non-Homogeneous Poisson Process Framework. IRAQI JOURNAL OF STATISTICAL SCIENCES, 22(2), 163–175. https://doi.org/10.33899/iqjoss.v22i2.54201