Donald Bren School of Information and Computer Sciences

This paper is concerned with evaluating the performability of degradable systems consisting of n primary modules and m spare modules, where all modules are identical. The existence of global spares violates the independence requirement of hierarchical composition modeling which is a common method for dealing with the state explosion problem. We consider the problem of calculating the probability that such a system is in a given performance level at time t when modules have arbitrary failure distribution. All known techniques for solving this problem are suitable only for small numbers of modules. Our analysis shows that the global spares dependence can still be handled satisfactorily using hierarchical composition modeling. Polynomial-time algorithms for calculating the probabilities that the system is in the highest performance level, and in any degraded level in the best and worst cases are presented. The algorithm to find the probability of the highest performance level also provides the first efficient solution for the reliability of non-degradable systems with global spares and arbitrary failure distribution.