Exact equations for the reliability and mean time to failure of 1-out-of-n cold-standby system with imperfect switching

Standby redundancy is a common and fundamental technique for increasing the reliability and availability of various systems. Cold-standby state is one of the most important strategies that are well used in non-repairable systems and plays an important role in mission-critical systems reliability, such as space exploration and satellite systems. In this paper, closed-form equations are derived using the Markov method to calculate the reliability function and the meantime to failure of a 1-out-of-n cold-standby system with non-repairable components under imperfect switching. While it is assumed that the failures of the switch and its associated active components are independent of each other, a constant failure rate is considered for the components and an increasing constant failure rate for the switch as it is used more frequently. In the end, numerical examples are solved for a system with various numbers of components to demonstrate the application of the closed-form equations.