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As electronic systems continue to evolve into more and more complex structures, the search for better and more efficient reliability prediction techniques naturally takes on added momentum. Needed are not only systematic methods of mathematical model building that will simplify the procedures involved but also noncomplex ways of obtaining solutions to many practical problems. This paper illustrates the applicability of transition diagram in describing the state space of a complex system, repairable or nonrepairable, and shows the methodology of writing the set of first-order linear differential equations representing the system performance by inspection of the transition diagram. A discussion of some applicable properties of linear signal-flow graphs is included. Methods of solving problems by inspection techniques are clearly explained and specific examples are given to illustrate the concepts. The mean time Tm for a system to pass for the first time from its initial state to a failed state is usually a statistic of prime interest. Certain properties of Laplace transform are used to illustrate how Tm of a general complex system, repairable or nonrepairable, can be obtained by solving a set of simultaneous algebraic equations. Flow graph techniques of solution by inspection are shown to be a valuable tool in obtaining analytical solutions for Tm of many practical systems.