In this paper, we analysed a system model which consists of two identical unit with the inspection of each unit. Each unit has three modes - normal (N), partial failure (P), and total failure (F). A unit can't enter into F-mode directly without passing through the P-mode. A single repair facility is always available with the system that inspects the partially failed unit first and decides whether to repair it on-line or off-line. A unit can't enter into F-mode during its on-line repair. The failure and inspection rates are taken as constants while the repair time distribution as general. Various important measures of system effectiveness are obtained by using the regenerative point technique.