Military Institutes of University Education Hellenic Naval Academy

Abstract: A deteriorating cold standby repairable system consisting of two dissimilar components and one repair-man is studied in this paper. Suppose that the life of each component satisfies the exponentially distribution and repair time of the component satisfies the general distribution, the component 1 has priority in use and repair. Firstly, a mathematical model is built via the differential and partial differential equations. And then using the C0-semigroup theory of bounded linear operators, the existence and uniqueness of the solution, the non-negative steady-state solution and the exponential stability of the system are derived. Based on the stability result, some reliability indices of the system and an optimization problem are presented at the end of the paper