Availability of an operating system during a given time interval: A dynamic programming approach

We consider the problem of running a one-unit failure system such that the probability that the system is operating over an entire prespecified time interval (or at least at some time instant during the interval) is maximized. A fixed number of unused units having identically distributed random operating times are at the controller's disposal. Simple assumptions are made on the stochastic failure mechanism. In particular, the time required to activate a unit for the system is supposed to be constant. Analyzing the associated dynamic programming equations yields closed-form solutions. © 1996 John Wiley & Sons, Inc.