Ensuring high-quality and uninterrupted power supply to consumers is one of the main problems of creating reliable power systems of a new generation. It is associated with the implementation of an integral assessment of the technical state of equipment of the power stations and substations, based on technical diagnostics data. Integral assessment involves the choice of ranges of the set of parameters of the technical state for groups of constituent elements of equipment, as well as the determination of their weight coefficients. Currently, the problem is solved with the help of expert assessments, arbitrarily in each specific case, which may lead to an incorrect integral assessment of the state of the equipment. The principle of decomposition makes it possible to determine the individual performance characteristics of each of them. At the same time, their subsequent aggregation ensures that the emergent properties of the system are taken into account. Such an approach was used in this work to evaluate individual types of equipment and their constituent elements. The algorithm for constructing a tree with a minimum random weight, proposed in this paper, makes it possible to increase the validity of decisions. They are made at various stages of designing complex technical systems and include tasks with an integral assessment of the technical state of equipment of power plants and substations. In the proposed algorithm, as a result of using the tree of variants, a matroid is formed, on which, using the “greedy” algorithm, the optimal solution can be determined.