A summary of optimum replacement policies for a parallel redundant system

Abstract This paper summarizes four replacement policies for an n-unit parallel redundant system. The system is replaced 1) at system failure or at time T1, 2) only at time T2, 3) at system failure or at time (j + 1)T if more than N1 units have failed until (j + 1)T, and 4) at time (j + 1)T if more than N2 units have failed until (j + 1)T. The expected cost rates for each policy are obtained and the optimum policies to minimize the expected costs are discussed. A numerical example is given when the failure times of units are exponential.