Cut sets

The result of the ETA is a Hst of combiaations of equipment and human failures that ate sufficient to result ia the accident (71). These combiaations of failures are known as minimal cut sets. Each minimal cut set is the smallest set of equipment and human failures that are sufficient to cause the accident if all the failures ia that minimal set exist simultaneously. Thus a minimal cut set is logically equivalent to the undesired accident stated ia terms of equipment failures and human errors. 

Fault Tree Solution. Solving the fault tree means obtaining the minimal cut sets. The minimal cut sets are all the combinations of equipment failures that can result in the fault tree TOP event. Computer programs are requked to determine the minimal cut sets for large fault trees (72). The solution method has four steps ... 

Minimal cut sets are then ranked. Two factors are considered in the ranking procedure. The first factor considers stmcture, ie, a one-event minimal cut set is more important than a two-event minimal cut set. The implication is that one event is more likely to occur than two events, two events are more likely than three events, and so on. The second factor considers ranking within equal-size minimal cut sets. The general ranking rules consider the probabihty of human error, active equipment failure, and passive equipment failure (73). 

J. B. EusseU, E. B. Henry, and H. N. MarshaU, MOCUS A Computer Program to Obtain Minimal Cut Sets from Fault Trees, Report 1156, Aerojet Nuclear Co., Idaho EaUs, Idaho, 1974. 

FTAP < characier " -ic nameSs rmation, scripiion AND K-of N NOT/ le computer meniory is limiting factor Minimal cut of up to 10 can be generated top-down, bo and Nelson memuu prime implicants f - i cut sets and [ji mic implicants Independent subtrees ibiind and replaced by inodijle IBM C sm 1IV, Available from Ope Rest Uni Cali ley... 

SETS FtUi J f. . rid). [. G 8). Adds generic causes and links to fault tree cutsets that include one or more generic causes are obtained and identified as common-cause candidates Can handle large fault trees and can identify partial dependency in cutsets attractive features of SETS as cut-set generator justify use for dependent failure analysis CDC 7600. AvaiJjhle Ifofn Argonne Softw-ie I en-i- r... 

Eliminating min cut sets with mutually exclusive events. 

RANK IMPORTANCE 1 5.622E-0I CUTSET MIN CUT SET PROBABILITY = 2.560E-03 NAME MEAN PROB rvajve 4.000E-01... 

In this study detailed fault trees with probability and failure rate calculations were generated for the events (1) Fatality due to Explosion, Fire, Toxic Release or Asphyxiation at the Process Development Unit (PDU) Coal Gasification Process and (2) Loss of Availability of the PDU. The fault trees for the PDU were synthesized by Design Sciences, Inc., and then subjected to multiple reviews by Combustion Engineering. The steps involved in hazard identification and evaluation, fault tree generation, probability assessment, and design alteration are presented in the main body of this report. The fault trees, cut sets, failure rate data and unavailability calculations are included as attachments to this report. Although both safety and reliability trees have been constructed for the PDU, the verification and analysis of these trees were not completed as a result of the curtailment of the demonstration plant project. Certain items not completed for the PDU risk and reliability assessment are listed. 

In connection witli fault trees, cut sets, and minimal cut sets are defined as follows. A cut set is a basic event or intersection of basic events that will cause the top event to occur. A minimal cut set is a cut set tliat is not a subset of any other cut set it may also be defined as the smallest combination of... 

The only cut set tliat is a subset is CG, which is a subset of G. Eliminating CG yields the following minimal cut sets ... 

The probability of the top set T is the probability of the union of the events represented by the minimal cut sets. This probability usually can be approximated by the sum of the probabilities of these events. Suppose that all tlie basic events are independent and tliat tlieir probabilities are... 

A runaway chemical reaction can occur if coolers fail (A) or if there is a bad chemical batch (B). Coolers fail only if both cooler 1 (C) and cooler 2 (D) fail. A bad chemical batch occurs if tliere is a wrong mi. (E) or a process upset (F). A wrong mi. occurs only if tliere is an operator error (G) and instrmiient failure (H). Construct a fault tree and obtain tlie minimum cut sets. 

This Area Cut Out to Allow Vapor Passage. Size of Cut Set by Combinations of Heat Transfer Coefficient and Pressure Drop. 

We assume that in a network there is at least one directed path from source to sink. A directed cut-set of a network is a set of directed edges such that every path from source to sink contains at least one... 

Theorem (Max-Flow, Min-Cut) The maximum flow between the source and the sink of a given network is equal to the minimum capacity of the cut-sets that separate the source from the sink.6... 

We first note that the flow can be resolved into flow through paths leading to the sink, each of which contains one dement of a cut-set, and into residual flow, which remains in some arcs of the network. 

Obviously, the total flow in the paths from source to sink cannot exceed the flow through the capacity of the cut-set. Hence, max (flow) min (cut-set capacity). To prove the equality we note that if no cutset exists all of whose arcs are filled to capacity, then we can produce by a constructive procedure, an unsaturated path in which one or more units of flow can be introduced, ultimately obtaining saturation of a set of arcs that contains a cut-set. This cut-set has minimum total capacity. 

Exercise By analogy with the above, obtain the cut-set matrix and show that a similar relation holds between the circuit matrix and the cut-set matrix. Note that the cut-sets that correspond to the rows of this matrix are ... 

There is an appropriate way of generating the cut-set matrix from the incidence matrix that requires considerable detail and involves the additional idea of a tree and of fundamental circuits and cut-sets. 

Current produced by single electron in a vacuum tube, 186 Curtiss, C. F., 1 Cut-set, 258 directed, 259 Cycle, 329 limit, 328 nonanalytic, 334 stable, 329 stable limit, 329 unstable limit, 329... 

Just as the incidence matrix M is related to material balances around each of (N - 1) vertices, the cut-set matrix K is clearly related to material balances around the (N - 1) vertex subsets VK (or VB, since material conservation holds over the whole network). In this case the (N — 1) vertex subsets happen to be a, e, c, (d, f, and f. ... 

Equations (16) and (17) show the important link between fundamental cycles and cut-sets of a graph. Thus, a spanning tree provides a convenient starting point for formulating a consistent set of governing equations for steady-state pipeline network problems. 

Fig. 10. Networks with pressure regulators (a) a cut-set formed by regulators, (b) regulators in a cycle. 

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