A simple universal generating function method for estimating the reliability of general multi-state node networks

Many real-world systems (such as cellular telephones, transportation, etc.) are Multi-state Node Networks (MNNs) that are composed of multi-state nodes with different states determined by a set of nodes receiving the signal directly from these nodes without satisfying the conservation law. Current methods for evaluating MNN reliability are all derived from Universal Generating Function Methods (UGFMs). Unfortunately, UGFMs are only effective for special MNNs without any cycle, i.e. acyclic MNNs. A very simple revised UGFM is developed for the general MNN reliability problem. The proposed UGFM allows cycles with the same time complexity as the best-known UGFM. The correctness and computational complexity of the proposed UGFM are analyzed and proven. One example is given to illustrate how MNN reliability is evaluated using the proposed UGFM.