In this paper, we identify an error in the proof of Theorem 1 in the paper Xia, L., Zhao, Q., and Jia, Q.S., “A Structure Property of Optimal Policies for Maintenance Problems with Safety-Critical Components”, IEEE Transactions on Automation Science and Engineering, 2008, 5(3): 519-531. Theorem 1 is the most important contribution of the above paper, which shows the optimality of the so-called ...