Note on reliability of a system complexity

Most systems have been recently complicated with remarkable development of their high performances. Both hardware and software become redundant, and sometimes, serious problems of interference between them might be newly generated. It would be inappropriate to calculate the reliabilities of such complex systems, using the usual computing method. In this paper, a measure of complexity is defined by the number of paths, and its reliability functions are given. Using this definition, the reliabilities of some typical redundant systems with complexity are obtained. Further, optimal numbers of components which maximize the reliabilities are given as numerical examples.