Optimal Reliability Allocation for Coherent Systems

In this paper, we consider a coherent system with specific structure and components selected from different batches. The batches include products with different reliabilities. We assume that the components of system in each position could be chosen from any batch. Under these conditions, the purpose is determination of the position of each component in the system such that the reliability of system has the desired level with the minimal imposed costs. This is known as the multi-objective optimization problem and we use the weighted sum method and goal programming approach to obtain an optimal solution. An example is given to illustrate the described model.