Redundancy allocation is one of the important approaches to increase reliability used by system designers. In this approach, to improve the reliability of the system, components or subsets (components) are considered in the system, which in case of failure of sensitive components of the system are quickly replaced and intermittently stop the operation of the system.
It is prevented. In this research, the problem of redundancy allocation for a system with one component with defined constraints and considering the cost of lost production is presented. In this article, the goal is to minimize the total cost of the system, which considers two strategies: cold plug-in and inventory. Cold plug-in refers to a situation where the surplus component is not normally under load and the probability of failure before replacing the damaged component is independent of system performance time. The decision variable in this study is the values ​​of the number of redundancy components and the stock of spare components in stock. The difference between the two is that the plug-in component quickly and without delay replaces the defective component in the system, and its presence does not stop during the maintenance of the main component. The mathematical planning model has been developed to achieve the objectives of the problem as a nonlinear complex problem. An example for the system is also given and solved by GAMS optimization software. Finally, the results of solving the model are discussed.