Work has been carried out for the reliability calculation of power generator for three subsystem Gi (i=1,2,3) and corresponding terminals Ti (i=1,2,3) connected in parallel redundant (1-out of 3-G and 3-T) along with three Main switch Board of power supplier they are connected with auxiliary switch board of power supplier and finally they all diverges on master switch board. Complex system configuration to be presented in Boolean algebra technique with development of mathematical modelling and expression of summation of axiomatic probability for an event has been explained. The logical Matrix has been also developed for reliability of the complex system with calculating Failure time, Mean time to failure(MTTF) for arbitrary distribution (Mainly exponential and Weibull) . Numerical example along with graphs among Reliability, Failure Time and MTTF has been also given for better understanding of model. Little observation has been also point out for the functioning of complex power system and its connectivity through main, common and auxiliary power supplier with corresponding terminal in new manners.