Evaluating equipment reliability function and mean residual life based on proportional hazard model and semi-Markov process

Based on Monte Carlo technique, a novel method is proposed to evaluate the reliability function (RF) and the mean residual life (MRL) of a power system component suffering from degradation. It is assumed that both the age and the health condition can affect failure rate. The Cox´s proportional hazard model (PHM) is used to customize the hazard rate of component with both age and health information. PHM consists of two parts: baseline function and link function. The baseline function represents the aging process and the link function represents the influence of covariant, such as the health condition. The health condition is divided into n-stages which confirms to a semi-Markov process. Based on the Monte Carlo technique, an algorithm is developed to find out the RF and MRL of a new or aging piece of equipment. We calculate the RF and MRL in the two cases respectively: (1) a new component and (2) an aging component survived until t₀. The case study shows that the proposed method can reflect the influence of both age and health condition on RF and MRL reasonably.