Reliability analysis of repairable system with arbitrary structure

In this paper, a general repairable system that the components have different failure rate and repair rate is studied. It is assumed that the repair rule of the failed components in the system is 'last-come-first-served', and every component after repair is 'as good as new'. Then, by using Laplace transform method, the unified state probability formulas of the general repairable system are derived; and some system reliability indices (or its Laplace transform), including the availability, the mean time to first failure, reliability, and rate of occurrence of failures, are obtained analytically. Moreover, the bounds of reliability indices are discussed since exact formulas are very complex. The results are shown that the determination of the maximum number of failed components such that the system can still work and the number of different cases that i components fail but the system still works are sufficient to derive the bounds of reliability indices.