Decisions on spare parts allocation for repairable isolated system with dependent backorders

The accuracy of spare parts allocation is essential for an isolated system performing its intended function and reducing the waste of resources. The backorders of different types of components for an isolated system are interdependent. The isolation time has a relatively large impact on the interdependent. Ignoring dependence among the component backorders will overestimate the spares stock for an isolated system. In this paper, we focus on backorder dependence to model spare parts allocation for an isolated system consisting of multiple types of components. We analyze the effect of isolation time on system availability and aggregate the backorder probabilities of the failed components to calculate the transition rate of available states for the rest of the functional components. We formulate the replenishment process of spare parts for the components in the isolated system using the state transition diagrams and matrixes. Multiple Markov processes are established for the multi-component isolated system considering backorder dependence. An optimization model of spares allocation for the isolated system is constructed with the constraint of the total spares cost considering the backorder dependence. We obtain the closed-form expression of the system stationary availability when the spare part reorder is sent out upon backorder occurrence. We find that the stationary availability function is a convex function. Several numerical examples of decisions on spare parts allocation for an isolated system is presented. We compare the output of our model with simulation software to verify the accuracy of the proposed method. The impact of prolonged isolation time on the expected number of backorders (EBO) is analyzed. We obtain higher availability for the isolated system with a lower stock level by employing the novel decision approach to spare parts allocation.