In this paper, a repairable multi-component system is studied where all the components can be repaired individually within the system. The whole system is inspected at inspection intervals and the failed components are detected and replaced with a new one, while the other components continue functioning. Replacing components individually within the system makes their initial age to be different at each inspection time. Different initial age of all the components have affect on the system reliability and probability of failure and consequently the optimal inspection time, which is for the whole system not individual components. A dynamic maintenance policy is proposed to find the next inspection time based on the initial age of all the components. Two competing failure processes of degradation and a shock process are considered for each component. In our paper, there is a mutual dependency between the degradation process and shock process. Each incoming shock adds additional abrupt damages on the cumulative degradation path of all the components, and the shock arrival process is affected by the system degradation process. A realistic numerical example is presented to illustrate the proposed reliability and maintenance model.