Optimization of Age Replacement Policy for Aging Multi-state System with Imperfect Maintenance

This article proposes the modified age replacement policy for a multi-state system composed of multi-state elements. The degradation of the multi-state element is assumed to follow the non-homogeneous continuous time Markov process which is a continuous time and discrete state process. A recursive approach is presented to efficiently compute the time-dependent state probability distribution of the multi-state element. The state and performance distribution of the entire multi-state system are evaluated via the combination of the stochastic process and the Lz-transform method. The concept of user-centered reliability measure is developed based on the system performance and the user demand. We develop the age replacement policy for an aging multi-state system subject to imperfect maintenance in a failure state. The optimum replacement schedule which minimizes the mean cost rate is derived analytically and discussed numerically.