An optimal maintenance time of automatic monitoring system of automatic teller machines with two kinds of breakdowns

All automatic teller machines (ATMs) in a bank operate unmanned on weekends and holidays, and an automatic monitoring system continuously watches the operation of ATMs through the telecommunications network. There are two kinds of trouble according to the installed places of ATMs. One is the trouble which occurs inside the branch of the bank where ATMs operate manned except on weekends and holidays, and the other is the one which occurs outside the branch where ATMs always operate unmanned. Two kinds of breakdowns are introduced, and the expected cost for an unmanned operation period is obtained. A maintenance policy which minimizes the expected cost is analytically derived. Finally, a numerical example is given and some useful discussions are made.