Semi-Markov Reliability Model of System Composed of Main Subsystem, Cold Backup Component and Switch

Probabilistic model of a system composed of a main component, an emergency backup component and the automatic switch are discussed in this paper. The reliability model is semi-Markov process describing evolution of the system. Conditional time to failure of the system is represented by a random variable denoting the first passage time of the process from the given state to the subset of states. The appropriate theorems of the Semi-Markov processes theory allow us to evaluate the reliability function and some reliability characteristics. To calculate the reliability function and mean time to failure of the system we apply theorems of the Semi-Markov processes theory concerning the conditional reliability functions.