The paper deals with the analysis of a system model consisting of two non-identical units. One unit is named as priority (p) unit and other as non-priority or ordinary (o) unit. So, initially priority unit is operative and the ordinary unit is kept into cold standby. Priority unit has three modes-Normal (N), Partial failure (P) and total failure (F) whereas ordinary unit has two modes-Normal (N) and total failure (F). The priority unit can’t enter into F-mode without passing through the P-mode. The operation and repair of priority unit in P-mode are possible simultaneously. A single repairman is always available with the system to repair priority unit failed partially or totally as well as the repair of totally failed ordinary unit. The preference in repair is being given to priority unit in both its partial and total failure mode over the ordinary unit. The joint distribution of failure and repair times of each unit is taken as bivariate exponential.System model is analyzed by using regenerative point techniqueto obtain various economic related measures of system effectiveness.