Statistical inference for dependent competing-risk failures in land-based radar detection: A PHW model under generalized progressive hybrid censoring

Hanan Haj Ahmad; Mohamed Aboshady; Ahmed K. Elsherif; Dina A. Ramadan; Hanan Haj Ahmad; Mohamed Aboshady; Ahmed K. Elsherif; Dina A. Ramadan

doi:10.3934/math.2025717

AIMS Mathematics

2025, Volume 10, Issue 7: 15991-16026. doi: 10.3934/math.2025717

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Statistical inference for dependent competing-risk failures in land-based radar detection: A PHW model under generalized progressive hybrid censoring

1.
Department of Basic Science, The General Administration of Preparatory Year, King Faisal University, Hofuf, Al-Ahsa 31982, Saudi Arabia
2.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia
3.
Department of Basic Science, Faculty of Engineering, The British University in Egypt, El Sherook City, Cairo, Egypt
4.
Department of Mathematics, Military Technical College, Cairo, Egypt
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 33516, Egypt

Received: 01 May 2025 Revised: 19 June 2025 Accepted: 07 July 2025 Published: 16 July 2025
MSC : 60G35, 62F10, 62F15, 62N01, 62N02, 62N05

Dependent competing risks usually arise in modern reliability and survival studies, but remain under‑explored because of the mathematical and computational complexity they introduce. This paper developed a flexible inferential framework for systems based on mutually dependent failure causes when the lifetimes are governed by the proportional hazard Weibull (PHW) distribution. Data were collected through the generalized progressive hybrid censoring scheme (GPHCS), which reduced test duration while preserving information with a prefixed number of failures. From a computational perspective, the maximum likelihood estimators (MLEs) were derived via numerical optimization, such as the Newton-Raphson algorithm. To incorporate prior knowledge and quantify parameter uncertainty, Bayesian estimates were produced using conjugate gamma priors and a Metropolis within Gibbs sampler. Estimator performance was assessed through an extensive Monte Carlo simulation study. Results show that MLE and Bayesian procedures were unbiased, and Bayesian credible intervals were noticeably shorter than their asymptotic counterparts. The procedure was applied to a land-based surveillance radar data set in which the target loss risks are dependent. The fitted PHW model accurately captures the dynamics of radar return signals, and posterior analyses revealed how each covariate modulates detection reliability.
- dependent competing risks,
- proportional hazard Weibull,
- generalized progressive hybrid censoring,
- maximum likelihood,
- Bayesian analysis,
- Monte Carlo simulation,
- radar signal
Citation: Hanan Haj Ahmad, Mohamed Aboshady, Ahmed K. Elsherif, Dina A. Ramadan. Statistical inference for dependent competing-risk failures in land-based radar detection: A PHW model under generalized progressive hybrid censoring[J]. AIMS Mathematics, 2025, 10(7): 15991-16026. doi: 10.3934/math.2025717

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Abstract

Dependent competing risks usually arise in modern reliability and survival studies, but remain under‑explored because of the mathematical and computational complexity they introduce. This paper developed a flexible inferential framework for systems based on mutually dependent failure causes when the lifetimes are governed by the proportional hazard Weibull (PHW) distribution. Data were collected through the generalized progressive hybrid censoring scheme (GPHCS), which reduced test duration while preserving information with a prefixed number of failures. From a computational perspective, the maximum likelihood estimators (MLEs) were derived via numerical optimization, such as the Newton-Raphson algorithm. To incorporate prior knowledge and quantify parameter uncertainty, Bayesian estimates were produced using conjugate gamma priors and a Metropolis within Gibbs sampler. Estimator performance was assessed through an extensive Monte Carlo simulation study. Results show that MLE and Bayesian procedures were unbiased, and Bayesian credible intervals were noticeably shorter than their asymptotic counterparts. The procedure was applied to a land-based surveillance radar data set in which the target loss risks are dependent. The fitted PHW model accurately captures the dynamics of radar return signals, and posterior analyses revealed how each covariate modulates detection reliability.

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