Optimal design of a maintainable cold-standby system

This paper considers a framework to optimally design a maintainable cold-standby system. Not only the maintenance policy is to be determined, but also the reliability character of the components will be taken into account. Hence, the mean time to failure of the components and the policy time of good-as-new maintenances are proposed as decision variables. Following probability analyses, the system cost rate and the system availability are formulated as the optimization object and the constraint, respectively. Then, this optimization problem is directly resolved by recognizing its underlying properties. Moreover, the resolving procedure is found to be independent of the failure distributions of the components and the forms of the system cost, which is illustrated through a numerical example. As a conclusion, an exact method is successfully established to minimize the cost rate of a cold-standby system with the given maintenance facility.