Innovative approaches in multistate network reliability modeling and computation

The two-terminal reliability (2TR) problem assumes a network and its elements can be in either a working or a failed state. However, many practical networks are built of elements that may operate in more than two states. Multi-state two-terminal reliability at demand level d (M2TR d) can be defined as the probability that system capacity, generated by multi-state components is greater than or equal to a demand of d units. This dissertation presents innovative algorithms that obtain the multi-state equivalent of binary cut and path sets, namely, multi-state minimal cut vectors (MMCV) and multi-state minimal path vectors (MMPV), for the M2TRd problem. These algorithms use an information sharing approach and a network reduction technique that significantly reduces the number of vector analyses needed to obtain all component levels that guarantee system failure/success. The algorithms mimic natural organisms in that a select number of MMCV (MMPV), called "offspring cuts" inherit information from other MMCV (MMPV) called "parent cuts."; Additionally, complexities related to the computation of reliability have been discussed. For some systems the computation of M2TR d may not be trivial. Three multistate network reliability bounding approaches, based on MMCV and MMPV, have been extended from well-known binary network reliability approximation methods. For these bounds, experimental results show that in some cases the approximated value may be far from accurate.; A new Monte-Carlo (MC) simulation approach that presents an accurate estimate of actual M2TR has been proposed. The method uses MC to generate system state vectors. These vectors are then compared to each MMCV to determine if system capacity satisfies the required demand. Results obtained from this approach consistently yield accurate M2TRd estimates while the accuracy of the bounding methods can be dependent on components that have considerable impact on the system design.; Finally, this dissertation presents composite importance measures (CIM) for multi-state systems. The proposed CIM are involved in measuring how a specific component affects multi-state system reliability. Currently, prioritizing system component importance, considering all of its states, is not clear using previously developed importance measures. CIM can be used as an effective tool to assess component criticality for multi-state systems.