Reliability of Some Modularly Redundant Systems

A mathematical model is established for the reliability of modularly redundant systems with unequal failure rates for the operating and standby units. The failure modes include failures of the active and standby units, three types of switch failures, and failures on system recovery. System reliability is considered for cases of both similar and dissimilar units, and for various restrictions on the failure parameters. It is shown that the most important failure parameters are those related to catastrophic failures, and that putting more reliable units as basic units, which operate initially, is important when switches and recovery are imperfect.