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

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.