COST EFFECTIVENESS ANALYSIS OF A SYSTEM COMPOSED OF TWO SUB- SYSTEMS
A complex system consisting of two sub-systems connecting in parallel mode has been considered in this paper. The first sub-system has two identical units with one as operative and other in cold standby mode while second sub-system has only one unit which is in operative mode. The failed units of sub-systems are subjected to repair. There is a single repair facility available with the systems which repair all the failed units with full satisfaction. There is also a inspection policy for units of first sub-system to check whether the repair is perfect or not. In case the repair is not perfect it requires post repair. The system will break down if both the subsystems failed. On failure of either of any sub system, system will work partially but with low efficiency. Therefore, system has three modes namely operating mode, partially operating mode and failure mode. The priority in repair is given to first sub-system if both the units of first subsystem are failed while priority is given to second sub system if any of the unit of first subsystem is operative. The Failure and repair time distributions are taken to be Rayleigh distribution but with different rates. Expressions for various measures of reliability have been obtained which help in studying of effectiveness of the system such as transition probabilities, mean time to system failure, availability, busy period of repairman and expected profit incurred.