Laplace Transforms for the Two-Unit Cold-Standby Redundant System

A conditional transform approach is applied to the two-unit standby redundant system with instantaneous switchover, and with failure and repair times that follow general well-behaved distributions for each unit. Transforms of distributions are obtained for T, the time to system failure, the number of repairs completed during T, the time spent on repair during T, and the idle time of the repairman during T. Applicable numerical methods are also discussed.