The paper deals with reliability analysis of a three non-identical complex unit system A, B and C arranged in such a way that the system failure occurs only if either unit-A fails or both the units B and C fail totally i.e. the units B and C are arranged in parallel network and this parallel sub-system of units B and C is arranged with unit-A in series network. There are two types of repairman: ordinary and expert repairman. The expert repairman is called only when system breaks down. Two types of repair facility is available to repair failed unit in which A gets priority for repair and is repaired by expert and B and C are repaired by ordinary repairman on first come first service basis. Further, if unit A is repaired by expert and during the process unit B or C fails, then that unit is also repaired by expert repairman till the system becomes operative.  The failure of units B and C are mutually dependent i.e. the unit-B fails with increased failure rate if the unit-C has failed. Similarly, the unit-C fails with increased failure rate if the unit-B has failed. The failure time distributions of unit-A is taken exponential. The distribution of time to failure of unit-B and unit-C are also exponential. The distribution of time to repair of unit-A, B and C is assumed to be general.