Analysis of a Semi-Markov Cold Standby System with Two Heterogeneous Components Considering Multiple Failure Modes

In this paper, a cold standby repairable system comprising two heterogeneous components, each characterized by multiple types of mutually independent failure modes, is investigated. The operational lifetimes of the components follow exponential distributions, while their repair times after failure are governed by general distributions. By applying the theory of the Markov renewal process together with the Laplace and the Laplace–Stieltjes transform techniques, we derive analytical expressions for the time to the first system failure, system availability, and the rate of occurrence of system failures. Some results for these reliability measures under several special cases are also presented. Finally, numerical examples are provided under different repair time distributions to analyze the influence of model parameters on the system’s reliability performance.