Robust Inference for Stress–Strength Reliability of the Garhy Distribution Under Diverse Record Schemes with Engineering and Medical Applications
4 affiliations
- 1Department of Mathematics, College of Science, University of Ha’il, Hail 55476, Saudi Arabia
- 2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
- 3Department of Mathematics, College of Sciences and Humanities, Prince Sattam Bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia
- 4Faculty of Computers and Information Systems, Egyptian Chinese University, Nasr City 4442126, Egypt
Abstract
This paper investigates the stress–strength reliability parameter R=P(Y<X) for the Garhy distribution under upper-, lower-, and mixed-record schemes. The Garhy distribution, a flexible one-parameter lifetime model, is shown to provide an excellent fit to precipitation and medical (kidney dialysis) data, with Kolmogorov–Smirnov p-values of 0.9904 and 0.9072, respectively. Maximum likelihood estimators (MLEs) of R are developed, alongside Bayesian estimators using Jeffreys and extended Jeffreys priors under squared error loss. Markov chain Monte Carlo (MCMC) methods are employed for posterior inference. An extensive Monte Carlo simulation study reveals that: (i) MLEs converge under all record schemes but exhibit larger bias and lower efficiency compared to Bayesian estimators; (ii) Bayesian estimators, in contrast, demonstrate superior stability, lower mean squared error, and better bias control, especially for pure upper and lower records; (iii) mixed records consistently yield the most balanced and reliable estimates, capturing distributional information more effectively than single-type records; and (iv) the extended Jeffreys prior provides effective bias correction, outperforming the standard Jeffreys prior in many scenarios. Analysis of real-world datasets confirms the simulation findings, with Bayesian estimators under mixed records producing stable and accurate reliability estimates, outperforming MLE in terms of precision and stability. The results strongly advocate for Bayesian methodology with non-informative priors when assessing stress–strength reliability from record-breaking data.
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BibTeX
@article{alenezy2026robust,
title = {{Robust Inference for Stress–Strength Reliability of the Garhy Distribution Under Diverse Record Schemes with Engineering and Medical Applications}},
author = {Abdullah H. Alenezy and Bassant Elkalzah and Anas F.I. Alharshan and Ghareeb A. Marei},
journal = {Mathematics},
year = {2026},
month = jun,
doi = {10.3390/math14111940},
url = {https://doi.org/10.3390/math14111940},
note = {CC BY},
}
RIS
TY - JOUR
TI - Robust Inference for Stress–Strength Reliability of the Garhy Distribution Under Diverse Record Schemes with Engineering and Medical Applications
AU - Abdullah H. Alenezy
AU - Bassant Elkalzah
AU - Anas F.I. Alharshan
AU - Ghareeb A. Marei
PY - 2026
DA - 2026/06/02
JO - Mathematics
DO - 10.3390/math14111940
UR - https://doi.org/10.3390/math14111940
AB - This paper investigates the stress–strength reliability parameter R=P(Y<X) for the Garhy distribution under upper-, lower-, and mixed-record schemes. The Garhy distribution, a flexible one-parameter lifetime model, is shown to provide an excellent fit to precipitation and medical (kidney dialysis) data, with Kolmogorov–Smirnov p-values of 0.9904 and 0.9072, respectively. Maximum likelihood estimators (MLEs) of R are developed, alongside Bayesian estimators using Jeffreys and extended Jeffreys priors under squared error loss. Markov chain Monte Carlo (MCMC) methods are employed for posterior inference. An extensive Monte Carlo simulation study reveals that: (i) MLEs converge under all record schemes but exhibit larger bias and lower efficiency compared to Bayesian estimators; (ii) Bayesian estimators, in contrast, demonstrate superior stability, lower mean squared error, and better bias control, especially for pure upper and lower records; (iii) mixed records consistently yield the most balanced and reliable estimates, capturing distributional information more effectively than single-type records; and (iv) the extended Jeffreys prior provides effective bias correction, outperforming the standard Jeffreys prior in many scenarios. Analysis of real-world datasets confirms the simulation findings, with Bayesian estimators under mixed records producing stable and accurate reliability estimates, outperforming MLE in terms of precision and stability. The results strongly advocate for Bayesian methodology with non-informative priors when assessing stress–strength reliability from record-breaking data.
SN - 2227-7390
ER -