Minimal Cut and Minimal Path Vectors in Reliability Analysis of Binary- and Multi-State Systems

Minimal Cut Vectors (MCVs) and Minimal Path Vectors (MPVs) are one of the principal tools of reliability engineering. MCVs represent situations in which repair/improvement of any system component results in functioning/ improvement of the system. MPVs coincide with circumstances under which failure/degradation of any system component causes system failure/degradation. MCVs and MPVs allow us to compute a specific measure known as FussellVesely’s Importance (FVI), which is used to evaluate importance of system components for system operation. The FVI has originally been developed for analysis of binary-state systems. In this paper, we propose several generalizations of this measure for multi-state systems. Furthermore, we summarize results from several papers focusing on identification of the MCVs and MPVs in multi-state systems and combine them with the proposed measures to develop a complex procedure for importance analysis of multi-state systems. The tool used for identification of the MCVs and MPVs is logical differential calculus.

[1]  Miroslav Kvassay,et al.  Minimal Cut Vectors and Logical Differential Calculus , 2014, 2014 IEEE 44th International Symposium on Multiple-Valued Logic.

[2]  Marvin Rausand,et al.  System Reliability Theory , 2020, Wiley Series in Probability and Statistics.

[3]  W. E. Vesely,et al.  A time-dependent methodology for fault tree evaluation , 1970 .

[4]  Elena N. Zaitseva,et al.  Multiple-Valued Logic mathematical approaches for multi-state system reliability analysis , 2013, J. Appl. Log..

[5]  J. B. Fussell,et al.  How to Hand-Calculate System Reliability and Safety Characteristics , 1975, IEEE Transactions on Reliability.

[6]  Antoine Rauzy.  Mathematical foundations of minimal cutsets , 2001, IEEE Trans. Reliab..

[7]  Wei-Chang Yeh.  A Fast Algorithm for Searching All Multi-State Minimal Cuts , 2008, IEEE Transactions on Reliability.

[8]  F. C. Meng.  Comparing the importance of system components by some structural characteristics , 1996, IEEE Trans. Reliab..

[9]  Way Kuo,et al.  Importance Measures in Reliability, Risk, and Optimization: Principles and Applications , 2012 .

[10]  David A. Butler.  A complete importance ranking for components of binary coherent systems, with extensions to multi-state systems , 1979 .

[11]  Miroslav Kvassay,et al.  Analysis of minimal cut and path sets based on direct partial Boolean derivatives , 2016 .

[12]  Wei-Chang Yeh.  Search for all d-Mincuts of a limited-flow network , 2002, Comput. Oper. Res..

[13]  Miroslav Kvassay,et al.  Minimal cut sets and direct partial logic derivatives in reliability analysis , 2014 .

[14]  Bent Natvig,et al.  Multistate Systems Reliability Theory with Applications , 2011 .

[15]  Weiwe-Chang Yeh.  A simple MC-based algorithm for evaluating reliability of stochastic-flow network with unreliable nodes , 2004, Reliab. Eng. Syst. Saf..

[16]  Wei-Chang Yeh.  Search for all MCs in networks with unreliable nodes and arcs , 2003, Reliab. Eng. Syst. Saf..

[17]  Jørn Vatn.  Finding minimal cut sets in a fault tree , 1992 .

[18]  Michal Kvet.  Index distribution management in attribute level temporal model , 2015, 2015 International Conference on Information and Digital Technologies.

[19]  Antoine Rauzy,et al.  New algorithms for fault trees analysis , 1993 .

[20]  Elena Zaitseva,et al.  Importance analysis of multi-state systems based on integrated direct partial logic derivatives , 2015, 2015 International Conference on Information and Digital Technologies.

[21]  Yi Ding,et al.  Multi-state System Reliability Analysis and Optimization for Engineers and Industrial Managers , 2010 .