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Peer-reviewedCC BYMathematics

Inference for Stress–Strength Reliability Under Unified Hybrid Censoring: A One-Parameter Model with Applications

  • Khudhayr A. Rashedi1
  • L. S. Diab2
  • Abdullah H. Alenezy1
  • Ghareeb A. Marei3
  1. 1Department of Mathematics, College of Science, University of Ha’il, Hail 55476, Saudi Arabia
  2. 2Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11432, Saudi Arabia
  3. 3Faculty of Computers and Information Systems, Egyptian Chinese University, Nasr City 4442126, Egypt
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Abstract

This paper addresses the estimation of the multi-component stress–strength reliability when both the strength variables and the stress variable follow the one-parameter Garhy distribution. Data are assumed to arise from a unified hybrid censoring scheme, which generalizes both Type-I and Type-II hybrid censoring. A closed-form expression for the reliability parameter Rm,k=P(atleastmof(X1,…,Xk)>Y) is derived, enabling efficient computation. Three estimation procedures are developed: maximum likelihood estimation (MLE), Bayesian inference using Markov chain Monte Carlo (MCMC) with non-informative priors, and the Tierney–Kadane Laplace-type approximation for posterior moments. For each method, we provide complete mathematical derivations, including the likelihood function under unified hybrid censoring, the posterior conditionals, and the asymptotic distribution of the reliability via the Delta method. Furthermore, Bayesian estimation is extended to asymmetric loss functions, and posterior propriety is formally proven. To check the suitability of the proposed methods, a real data application on generator failure times in power systems is presented.

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Cite

BibTeXRIS
BibTeX
@article{rashedi2026inference,
  title = {{Inference for Stress–Strength Reliability Under Unified Hybrid Censoring: A One-Parameter Model with Applications}},
  author = {Khudhayr A. Rashedi and L. S. Diab and Abdullah H. Alenezy and Ghareeb A. Marei},
  journal = {Mathematics},
  year = {2026},
  month = jun,
  doi = {10.3390/math14122041},
  url = {https://doi.org/10.3390/math14122041},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Inference for Stress–Strength Reliability Under Unified Hybrid Censoring: A One-Parameter Model with Applications
AU  - Khudhayr A. Rashedi
AU  - L. S. Diab
AU  - Abdullah H. Alenezy
AU  - Ghareeb A. Marei
PY  - 2026
DA  - 2026/06/08
JO  - Mathematics
DO  - 10.3390/math14122041
UR  - https://doi.org/10.3390/math14122041
AB  - This paper addresses the estimation of the multi-component stress–strength reliability when both the strength variables and the stress variable follow the one-parameter Garhy distribution. Data are assumed to arise from a unified hybrid censoring scheme, which generalizes both Type-I and Type-II hybrid censoring. A closed-form expression for the reliability parameter Rm,k=P(atleastmof(X1,…,Xk)>Y) is derived, enabling efficient computation. Three estimation procedures are developed: maximum likelihood estimation (MLE), Bayesian inference using Markov chain Monte Carlo (MCMC) with non-informative priors, and the Tierney–Kadane Laplace-type approximation for posterior moments. For each method, we provide complete mathematical derivations, including the likelihood function under unified hybrid censoring, the posterior conditionals, and the asymptotic distribution of the reliability via the Delta method. Furthermore, Bayesian estimation is extended to asymmetric loss functions, and posterior propriety is formally proven. To check the suitability of the proposed methods, a real data application on generator failure times in power systems is presented.
SN  - 2227-7390
ER  -