A Method for Computing Complex System Reliability

Enumeration of Minimal Cutsets for Directed Networks with Comparative Reliability Study for Paths or Cuts

“…Although, there are plethora of methods available that deal with evaluation of these measures yet for most large and complex networks, the path/cutsets‐based SDP techniques have appeared to be simple and efficient as compared to other available techniques. There are several researchers, who have employed path/cutsets for 2 ‐terminal reliability evaluation either using inclusion/‐exclusion or SDP technique assuming either nodes are perfectly reliable or by relaxing this assumption . The evaluation of overall reliability based on the spanning trees of the reliability graph of the network and then expressing this enumeration as a Boolean algebraic statement are suggested by Rai .…”

Algebraic Aspects of Computing Network Reliability.

“…In a typical situation, edges of the network (which may be directed or undirected) are assumed to fail in a statistically independent fashion with known probabilities. For such networks, a variety of probabilistic measures of system performance have been considered: namely, the probability that two given nodes can communicate [11,13,33], that a given node can communicate with a specified portion of the network [6,25], or that every pair of nodes can communicate [8,26,33].…”

“…One class of methods is based on the idea of a path, a minimal set of edges whose operation ensures that the system functions. In this approach, paths must first be enumerated and then combined either by applying the inclusion-exclusion principle or by effecting a partition into mutually disjoint events [2,[13][14][15]17,27]. An alternative approach uses instead the enumeration and combination of cutsets, minimal sets of edges whose failure ensures that the system cannot function [1,11,12,17,22].…”

An Efficient Method for Reliability Evaluation of a General Network

“…reliability expression using probability theory, Boolean algebra, graph theory, etc. Various techniques exist in the literature to deal with NOTATION the problem of path enumeration in a general network. Some of them [3,4] have used powers of connection ma-k total number of nodes trix to determine the paths. This method requires (k-1) nj node j (j=1 is source) matrix multiplications where k is the number of nodes in b total number of branches the graph.…”

“…Refs. [3,4] show a 0 X5 X7 1 X8 method to find paths using the connection matrix. The connection matrix is defined as an analytic correspond-Expand (2) in accordance with step 4: ence of the system graph and has a size k x k. An important s = X1X3X6X7X8 u XlX3X6X9 u XlX3X5x8 u XlX3X5X7X9 property of this matrix is: Entry in ninj position of matrix u X1X4X8 u XlX4X7X9 U XlX4X5X6X9 U X2X6X7X8…”