Reliability and availability of redundant systems: Computational program and the use of nomograms

A rigorous mathematical approach to determining the reliability and availability of repairable actively redundant systems - (r/m) systems - is considered for the case where the m units comprising the system are identical and the failure and repair rates, lambda and μ respectively, are constant. The method used involves the Markov processes, operator calculus and matrix calculus. All the results of the study are handled by the FIDIAS program, which is a practical tool for calculating with a high degree of precision the reliability or availability of such (r/m) systems whatever the values of m and r. In the FIDIAS-TC version of FIDIAS it is possible to plot curves with a Benson plotter, so that nomograms are produced for rapid and simple determination of the probabilities of failure or non-availability of the (r/m) systems considered. The practical application of nomograms is of interest because (2/3) and (2/4) actively redundant systems are very often used in the control circuits of power reactors. It is shown how easily one can compare these two systems using nomograms and how one can determine lambda or μ as a function of the anticipated result