A review of proportional hazards models for health prognostics of deteriorating systems

Abstract As modern engineering systems become increasingly complex, predicting their remaining useful life and detecting early signs of degradation have become critical. Among various health prediction methods, the proportional hazards model supports health prognostics by linking baseline hazard and covariate processes to system hazard rates. Notably, the covariate processes of proportional hazards models can be modeled as Markov process, Wiener process, Gamma process and other stochastic processes to effectively describe the degradation trend under dynamic environmental conditions. This has led to widespread applications of proportional hazards models in health prognostics. However, recent research lacks a comprehensive review of the current status, emerging trends and challenges associated with proportional hazards model-based health prognostics for deteriorating systems. This paper addresses this gap by systematically introducing the fundamental structure of proportional hazards model, including its baseline hazard function, link function, and covariates, and two approaches to model parameter estimation for this model. Subsequently, existing works on health prognostics using proportional hazards models are considered, and different variants of proportional hazards model-based prognostic methods are reviewed. Applications of the proportional hazards model in health prognosis are also investigated. Finally, the conclusions are presented, and future research challenges are discussed.