This paper presents a model for optimizing maintenance plans for an industrial system consisting of a number of assets with degradation and performance interaction between them. In particular, we consider an asset system with M identical non-critical machines feeding their output to a critical machine. A common repair team performs maintenance on all the machines. All the machines deteriorate over time stochastically independently. In addition to the stochastically independent degradation, the degradation of the non-critical machines also affects the performance of the critical machine. We develop a mathematical model to represent these interactions and performance of the asset system. We also provide a simulation-based numerical solution to optimize the maintenance plan for the system outlining the maintenance intervals for each of the machines.