A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory

•A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory is described.•The issue studied in this paper comes from the practical flattener control system in a steel plant.•Optimal preventive maintenance cycle corresponding to the maximum of mean time to system failure is derived.•All the maximums of MTSF obtained are higher than the scheme of Mahmoud and Moshref (2010).•The optimal results obtained have been applied to the PM policy of the flattener control system.

A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy.