A recursive method for the health assessment of systems using the proportional hazards model

The failure of many practical systems is dependent on both age and a diagnostic covariate process. Cox's proportional hazards model is widely adopted to describe the failure rate of such systems. If the covariate state space is large, it is computationally not feasible to use an analytical method for health assessment at inspection epochs. Existing approximation methods, although can address the above problem, fail to satisfy the critical requirements of modern health management in terms of accuracy, memory storage, and computational speed. This paper develops a novel recursive method to approximately assess the health indices of the proportional hazards model with a Markovian covariate process. The method discretizes age into equidistant and small subintervals. Over each subinterval, an incomplete state transition matrix is constructed with each element measured by its upper and lower bounds. The consideration of dual bounds makes our model more robust than previous methods considering only an upper bound. Then the recursive formulas of various health indices are derived based on the matrixes of consecutive subintervals. Two practical examples demonstrate that the proposed method can produce accurate assessment results with higher efficiency and less memory compared with existing approximation methods.