Evaluation of Reliability Function and Mean Residual Life for Degrading Systems Subject to Condition Monitoring and Random Failure

This paper presents a new general method for evaluating the reliability function and the mean residual life of degrading systems subject to condition monitoring and random failure. In the proposed method, the degradation process of the system is characterized by a continuous-time Markov chain, which is then incorporated into the proportional hazards model as a stochastic covariate process to describe the hazard rate of the time to system failure. Unlike the conventional method based on conditioning, which is applicable only for a small number of degradation states, the proposed method is capable of tackling the case with a general number of degradation states. Using the developed approximation techniques, closed-form formulas for related reliability characteristics are obtained in terms of the appropriate transition probability matrix. The proposed evaluation algorithm is computationally efficient and embeddable to support real-time reliability assessment of the system subject to condition monitoring for developing the optimal maintenance policy. The effectiveness and the accuracy of the method are validated by a numerical study and compared with the conventional method. A general case where the degradation path can be discretized up to ten states is also studied to illustrate the appealing general features.