Abstract: Health assessment is of crucial significance for prognostics and health management. Its accuracy relies heavily on the failure mechanism of the system under consideration. Proportional hazards models are widely adopted in reliability engineering for describing the joint effects of age and covariates on failure time. In many practical situations, the covariate progress is stochastic, making it of great challenge to assess the health state of a system in the proportional hazards model. An iteration method is developed to approximately address the problem of health assessment in the proportional hazards model with a Markovian covariate process. First, the one-step transition probability matrix for the joint process of age and covariate is constructed. Based on the state-transition properties of consecutive time units, the calculation formulas of some health indices such as conditional reliability and remaining useful time are provided with proof. The effectiveness of the proposed approach is verified by two practical examples. In example 1, the comparison with the analytical method shows that the accuracy is increasing with the increase of discretization level, and a recommendation for determining a discretization level is provided. In example 2, the comparison with the transition matrix method shows that the proposed recursive method can produce accurate estimations efficiently with low memory requirements.

Key words: proportional hazards model, health assessment, conditional reliability, mean residual life, recursive algorithm