Multi-state Two-Terminal Reliability: A Generalized Cut-Set Approach

This paper describes an extension of a classical network reliability problem to the multi-state case. 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. The major focus of this study is to develop a methodology for obtaining the multi-state equivalent of binary cut sets, namely, multi-state minimal cut vectors (MMCV), for the multi-state two-terminal reliability (M2TR) problem. The algorithm uses an information sharing approach that significantly reduces the number of vector enumerations needed to obtain all MMCV. The algorithm mimics natural organisms in that a select number of MMCV, called “offspring cuts,” inherit information from other MMCV called “parent cuts.” Additionally, the paper discusses the computation of reliability once the MMCV are known. For large systems with even a relatively small number of states, the computation may not be trivial, and simulation is discussed as a useful approach to obtain fairly accurate approximations. This paper presents preliminary results on a straightforward Monte Carlo simulation to approximate M2TR. Examples are included to illustrate the methodology.