[en] The fundamental concepts and relations that should be used in the reliability analysis of systems with numerous components are discussed, with an emphasis on calculable quantities. These are: (1) the average probability of being in a state, (2) the average transition rates between states, in the long run or as time functions, and (3) the integrals of the transition rates, which are the expected numbers of transitions. These quantities are related by the net transition relations, and the calculationally vital transition rate relation when the inputs of an item are statistically independent. Assumptions necessary for the existence of these quantities and for the relations are listed, and proofs given. The importance of exploiting the closeness to ''simple'' structure which systems may possess, and the versatility for different problems of a computational technique of ''reduction'' and ''expansion'' are discussed. The key relations for the latter are formally derived. Applications are made to fault trees, structure networks, undirected and directed communication networks