Reliability analysis of a two identical components cold standby system with multiple failure modes

As technological equipment grows in complexity, systems may encounter failures caused by hardware, software, environmental, human, and other factors, leading to diverse manifestations of system failures. In fact, reliability models with multiple failure modes can provide a more precise and nuanced characterization of system behavior. This article considers a two identical components cold standby repairable system where the operating component has c failure modes, and the repair time of the failed component has a general distribution. Employing the Markov renewal process theory, the Laplace transform, and the Laplace-Stieltjes transform, we derive analytical solutions of the mean time to the first system failure, the system availability, and the rate of occurrence of system failures. Further, two special cases of the two identical components cold standby system with two failure modes and the two identical components cold standby Markov system are discussed. Moreover, some numerical examples are provided to discuss the influence of system parameters on reliability measures.