A generalized multistate-based path vector approach to multistate two-terminal reliability

The two-terminal reliability problem assumes that a network and its elements are either in a working or a failed state. However, many practical networks are built of elements that may operate in more than two states i.e., elements may be degraded but still functional. Multistate two-terminal reliability at demand level d (M2TR_d) can be defined as the probability that the system capacity generated by multistate components is greater than or equal to a demand of d units. This paper presents a fully multistate-based algorithm that obtains the multistate equivalent of binary path sets, namely, Multistate Minimal Path Vectors (MMPVs), for the M2TR_d problem. The algorithm mimics natural organisms in the sense that a select number of arcs inherit information from other specific arcs contained in a special set called the "primary set." The algorithm is tested and compared with published results in the literature. Two features of the algorithm make it relevant: (i) unlike other approaches, it does not depend on an a priori knowledge of the binary path sets to obtain the MMPVs; and (ii) the use of an information sharing approach and network reduction technique significantly reduce the number of vector analyses needed to obtain all the component levels that guarantee system success. Additionally, the complexities associated with the computation of reliability are discussed. A Monte Carlo simulation approach is used to obtain an accurate estimate of actual M2TR values based on MMPVs. Examples are used to validate the algorithm and the simulation procedure.