Minimal-Cut Reliability Lower-Bound for Systems Containing Standby Modules

Standby redundancy is often present in systems whose reliability is to be evaluated. The well known minimal-cut reliability lower-bound is shown to be valid for a s-coherent system containing standby modules; this is done by demonstrating that the joint performance-process of system devices is time-associated. As in practice one often assumes that performance processes of modules and components constituting the system are s-independent, for the joint process to be time-associated, it is sufficient to demonstrate time-association for the performance process of each system device. We verify that this property is possessed by the performance process of a standby system formed from i.i.d. components. Two different approximations are derived for the reliability of a minimal-cut containing a standby module. One is easily calculable and then suitable to save computer time when calculating the distribution of time to first system failure. This approximation is compared with the rough one obtained considering the standby module as if it were a parallel system.