Using a new algorithm based on the (UGF) technique and a partitioning of these systems, we will present an understanding of the mathematical relationships that can aid in the computation of the reliability of mixed block diagrams (systems) and the complex-parallel systems. In subsystems and determining the mathematical link between these groups as well as the reliability of each subsystem that makes up this system. The reliability importance of mixed block diagrams was calculated, as well as the reliability importance of the subsystem's complex-parallel systems, to arrive at mathematical relationships that achieve the reliability importance of complex-parallel systems. This implies that we won’t have to compute the sums for the original system if we understand how to calculate these sums for partial systems. This saves time, effort, and computations necessary to determine reliability. Mathematica software is used to write all algorithms and computations.