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. component i i =1, 2 the cumulative distribution function (CDF) of component lifetime the CDF of repair time for failed component the CDF of maintenance time the failure rate of components the repair rate, the mean of G 1(t) the maintenance rate, the mean of G 2(t) the random variable denoting component lifetime the random variable denoting repair time the random variable denoting maintenance time the PM cycle the optimal PM cycle the random variable denoting T the CDF of X T the CDF for system transits from regenerative state S i to S j the CDF of time from entering S i to system failure the mean of π i (t) the states space E ={S i ∣i =0, 1, 2, 3} the convolution operator the symbol denoting the result of Laplace transform for a variable 
A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory