The purpose of the paper is to make profit analysis of a two unit priority system with two types of repair facility and proviso of rest. The proposed system model consists of two units where in one unit is priority and other is non priority unit. Initially the priority unit is in operative mode while the non priority unit is in standby mode. On failure of the priority unit the standby non priority unit becomes operative and the failed priority unit is put under repair immediately. The non priority unit may work up to a certain time which is called maximum allowable time. The non priority unit is put under rest after the maximum allowable operative time even if the repair of the priority unit is in progress. There are two types of repair facilities i.e. ordinary repairman and expert repairman. The expert repairman is called on need base, i.e. the expert repairman is called only when the ordinary repairman fails to repair the failed priority unit. The non priority unit is always repaired by ordinary repairman. By regenerative point technique, the various important measures of system effectiveness have been obtained.