Asymptotic unavailability for an M-out-of-N system without testing

Abstract

A simple closed form equation is presented for the asymptotic unavailability of a system consisting of N identical units of which M are required for operation. Nonoperating units can fail during standby, and at most R failed units can be under repair at any time. A Markov model is assumed, e.g. the units fail randomly and require a random time interval for repair; there are no periodic inspections or tests. The equation has useful pedagogical applications since there are six independent variables that can be changed.