An optimal maintenance time of automatic monitoring system of ATM 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 telecommunication network. There are two kinds of troubles according to the installed places of ATMs. One is the trouble which occurs inside the branch of a 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.