The parallel system can be regarded as a multi-state system withgraduate failure. When the system is not in its perfect state, it can be repaired to some higher level under some cost, in our case, to repair k components costs C0 + kC1. The objective of this research is to find the optimal repairing policy, so that the system makes the greatest possible profit. The main idea of the optimal solution is based on the analysis of the system performance during periods with a certain length, which allows us to use dynamic programming as optimizing technique. Additionally for the systems with unlimited working time we give a way for computation of the optimal repairing level.
Optimal profit, multi-state system, parallel system.