JOINT DISTRIBUTION OF UPTIME AND DOWNTIME FOR SOME REPAIRABLE SYSTEMS

Abstract

An uptime and a downtime for some redundant repairable systems are not independent each other. The joint distributions of a single uptime and a single down-time for such systems are derived by using renewal equations . In particular, the downtime distributions are easily obtained by the marginal distributions of the joint ones. Explicit forms of the joint distributions are obtained for a few systems.