Upper Bounds on Mean Life of Self-Repairing Systems

Upper bounds on mean life of self-repairing systems are established on the basis of a very general system model. Expressions for system mean-life are obtained by formulating the problem as a two-dimensional difference equation in time and the number of nonfailed spare elements. Results indicate that mean life of an isolated system cannot be expected to exceed roughly three times the mean life of the elements which make it up, regardless of how standby elements are employed. If the element failure rate in standby is substantially less than the failure rate in operation, then system mean life is essentially linearly proportional to the number of available standby elements.