This paper deals with a continuously deteriorating system which is inspected at random times sequentially chosen by help of a maintenance scheduling function. The deterioration is modeled by a Gamma process. The system is considered as failed if its condition jumps above a pre-set failure level. Two types of replacement can take place at each inspection date depending on whether the current system state is above a pre-set critical threshold but not failed or in the failed state. This paper is focused on the development of a new probabilistic method based on the semi-regenerative property of the evolution process in order to calculate the long-time expected cost per unit of time. We use a recent result generalizing the well-known theorem usually used which says that the cost criterion is equal to the ratio of the expected cost on a renewal cycle over the expected cycle duration. Numerical experiments show that there exists a set of parameters (the critical threshold and the parameters of the maintenance scheduling function) which lead to a minimal cost.