Here, a complex system consisting two sub-systems connected in series is analyzed stochastically in detail by using regenerative point technique. The first sub-system has only one unit A which is initially operative and the second system has two units (B & C) connected in parallel. The system is considered as operative when unit A of the first system and at least one unit B & C of second sub-system are in working conditions. A single repairman is made available to handle the repair activities. The unit-A undergoes for inspection after repair to ascertain whether the repair is perfectly done or not. In case repair of the unit-A is not found perfect then it goes for post repair. The first come first serve discipline policy for repair is followed in the system. However, if one unit of second sub-system is an operative mode and other is under repair then priority is given to the repair of the unit-A of the first sub-system over unit of second sub-system. Several measures of system effectiveness are studied to see their impact on the system performance and thus reliability of the system. The distributions for failure times is taken as negative exponential while arbitrary distributions are considered for the random variables associated with different time points. The measures transition probabilities, mean time to system failure, availability, busy period of the repairman, expected number of the visits of the repairman and profit function are obtained under different parametric values of the random variables associated with failure, repair and inspections times. The behavior of some important measures has been observed through graphs.