Analysis of Noncoherent Systems and an Architecture for the Computation of the System Reliability

A k-to-/-out-of-n system is a noncoherent system in which no fewer than k and no more than l out of n units are to function for the successful operation of a system. Examples of noncoherent systems are found in multiprocessor, communi-cation, and transportation applications. A noncoherent system is very general and includes the parallel, series, and N-modular redundancy systems as special cases. The reliability of noncoherent systems has been analyzed by several researchers but the number of computational steps for the evaluation has not reached the minimum. Earlier techniques based on the generalizations of the inclusion-exclusion principle and the event-space approach for computing reliability are inef-ficient. After briefly reviewing these and some of the recent and more efficient techniques, an alternative approach based on the elementary event method is presented for computing the reliability of noncoherent systems. A salient feature of this new technique is its adaptability to a simple cellular realization in hardware. This cellular implementation improves the computational complexity from quadratic to linear-order time. Theoretical results on the optimization issues of noncoherent systems are also presented.