Multistate two-terminal reliability: A cut-set approach

Jose E. Ramirez-Marquez, David W. Coit

Research output: Contribution to conferencePaperpeer-review

1 Scopus citations


This study 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, in some cases binary state theory does not fully characterizes actual system reliability behavior [6]. For networks whose elements may operate in any of several intermediate states, betterresults may be obtained using a multi-state reliability approach. The 2TR problem is formulated and analyzed assuming the links in the network may each operate in one of several degraded states. Thus, the reliability behavior of the network as a whole is also viewed as multi-state. 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 motivation behind the methodology is twofold. First, a binary minimal cut vector is still a cut vector in the multi-state case, although it may not be minimal. That is, the level, xi, at which the arcs belonging to the binary cut are functioning may not be minimal when considering multi-state behavior. Thus, the problem in the multi-state case reduces to finding the minimal state levels of the components in the binary cut. Algorithms previously developed use this property to construct the MMCV. Second, when the network under consideration has no cycles, information sharing among the cuts is an advantage that can significantly reduce the number of enumerations needed to obtain MMCV. Based on the binary minimal cut sets, previous algorithms use an exhaustive enumeration approach to find the new component states of a given binary cut that entail system failure in the multi-state case. Alternatively, the approach presented in this paper identifies two basic cuts, called parent cuts, which propagate information (component states) to a specified number of binary cuts called offspring 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 Monte Carlo simulation to approximate M2TR. Examples are included to illustrate the methodology.

Original languageEnglish (US)
Number of pages1
StatePublished - 2004
EventIIE Annual Conference and Exhibition 2004 - Houston, TX, United States
Duration: May 15 2004May 19 2004


OtherIIE Annual Conference and Exhibition 2004
Country/TerritoryUnited States
CityHouston, TX

All Science Journal Classification (ASJC) codes

  • Engineering(all)


  • Multistate
  • Network
  • Reliability


Dive into the research topics of 'Multistate two-terminal reliability: A cut-set approach'. Together they form a unique fingerprint.

Cite this