In general, downtime of a system can be attributed due to multiple failure categories and repair costs for each failure categories can be different. Many of these failure types are repaired to a state which can be called as bad as old and such repair actions are termed as “minimal repair”. Many system or components are replaced after a certain number of such minimal repair actions. In this study, we intend to prove that if the system failure process can be described by NHPP (Non Homogenous Poisson Process), then each failure category can also be modelled by NHPP.

Based on this, a cost model is developed by using the decomposition of the NHPP and renewal theory. Using the cost model, a model is developed to obtain the optimal number of minimum repair action every failure category. Since it is not possible to find any analytical solution, solution to the renewal function, an approximate approach is introduced to obtain numerical solution. Finally, a numerical example is presented to demonstrate the method.