Optimal replacement policy for safety-related multi-component multi-state systems

This paper investigates replacement scheduling for non-repairable safety-related systems (SRS) with multiple components and states. The aim is to determine the cost-minimizing time for replacing SRS while meeting the required safety. Traditionally, such scheduling decisions are made without considering the interaction between the SRS and the production system under protection, the interaction being essential to formulate the expected cost to be minimized. In this paper, the SRS is represented by a non-homogeneous continuous time Markov model, and its state distribution is evaluated with the aid of the universal generating function. Moreover, a structure function of SRS with recursive property is developed to evaluate the state distribution efficiently. These methods form the basis to derive an explicit expression of the expected system cost per unit time, and to determine the optimal time to replace the SRS. The proposed methodology is demonstrated through an illustrative example.