Quantitative Network Engineering with Fault Tree Analysis
This is a simple paper outlining how to use some Risk Analysis Techniques with Network Engineering to obtain quantitative results. An attempt to turn network engineering from an artful guessing game into a science.
Jumping back to the analysis of the Blackhole Networks Router system, a top-down
analytical method will be used to systematically find the cutsets. This will use the matrix style approached outlined by P.L. Clemens (see references).
The first step in this approach is to create a matrix and place the label of the top gate at the upper left corner.
A spreadsheet is really helpful here. The top gate in our fault tree has been labelled as 1.
Place the top Gate at the top of the matrix:
1
The next step examines the type of gate, and replaces it with any contributing events or gates. If the gate being replaced is an AND gate,
it is replaced horizonally with the labels of the contributers. If the gate is an OR gate, it is copied and replaced vertically with the contributers.
Since Gate 1 is an OR gate, with three input gates of 2, 3, and 4, our matrix looks like the following after the rows have been copied and the
substitutions made:
2
3
4
The rest of the analysis is more or less an iterative process whereby each gate is replaced, copied and substituted with it's contributors
until what remains are only basic events. In the example: Gate 2 is an OR gate, so it is copied vertically and input gates of 5 and 6 are
substitued in it's place; Gate 3 is an AND gate, so it is replaced horizontally with it's inputs of gate 7 and 8; and gate 3 is an OR gate
with inputs of basic event A and gate 9.
5
6
7
8
A
9
Note that now we have a basic event listed in our developing cutsets. This can't be broken down any further, but we need to continue on with
breaking down the gates further. In the next step Gate 5 is an AND gate, so it is replaced with the two gates that feed it horizontally --
10 and 11. Gate 6 is an OR gate, so it is copied and replaced vertically with basic event K and gate 12. Gate 7 is an OR gate, it is
replaced and copied vertically with basic event F and gate 14. Gate 9 is an AND gate, so it is substituted with it's inputs which are
gates 15 and 16.
10
11
K
12
F
8
14
8
A
15
16
The rest of the process continues to iterate, and can get tiresome and repetitive. So the remaining section can be skipped over unless
the method of analysis needs to take firmer root. In the next step: Gate 10 is an OR gate, so replace it vertically with Gates 17, 18
and basic event O. Gate 12 is a 2/3 voting gate which is essentially a combination of an OR and and AND gate,
so replace it vertically with basic events L, M, N and horizontally with L, M, N. Gate 14 is an OR gate so replace it with basc events
I and J. Finally, gate 15 is an OR gate so replace it with basic events B and C.
7
11
18
11
O
11
K
L
M
N
M
N
L
F
8
I
8
J
A
B
16
C
16
Contining: Gate 17 is an OR Gate, replace it with basic events P, Q and gate 21. Gate 18 is an OR Gate, replace it with basic events
R and S. Gate 8 is an OR gate, so replace it vertically with basic events G and H. Gate 16 is an OR gate so replace it with
basic events D and E.
P
11
Q
11
21
11
R
11
S
11
O
11
K
L
M
M
N
N
L
F
G
F
H
I
G
I
H
J
A
B
D
B
E
C
D
C
E
Gate 21 is an OR Gate so copy it and replace it vertically with basic events H and T.
P
11
Q
11
H
11
T
11
R
11
S
11
O
11
K
L
M
M
N
N
L
F
G
F
H
I
G
I
H
J
A
B
D
B
E
C
D
C
E
Gate 11 is an OR gate, so replace it and copy it vertically with Gates 19, 20 and basic event U.
P
19
P
20
P
U
Q
19
Q
20
Q
U
H
19
H
20
H
U
T
19
T
20
T
U
R
19
R
20
R
U
S
19
S
20
S
U
O
19
O
20
O
U
K
L
M
M
N
N
L
F
G
F
H
I
G
I
H
J
A
B
D
B
E
C
D
C
E
Gate 19 is an OR gate, so replace it vertically with basic events V, W and Gate 22.
Gate 20 is an OR gate, so Replace it vertically with basic events X and S.
P
V
P
W
P
22
P
X
P
S
P
U
Q
V
Q
W
Q
22
Q
X
Q
S
Q
U
H
V
H
W
H
22
H
X
H
S
H
U
T
V
T
W
T
22
T
X
T
S
T
U
R
V
R
W
R
22
R
V
R
W
R
U
S
V
S
W
S
22
S
X
S
S
S
U
O
V
O
W
O
22
O
X
O
S
O
U
K
L
M
M
N
N
L
F
G
F
H
I
G
I
H
J
A
B
D
B
E
C
D
C
E
And finally, eliminating the last of our gates we replace gate 22 vertically with basic events H and Y.
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| Version 0 | C | Plenty |
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| Router ID - www.blackhole-networks.com |
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| Area ID - FTA with Network Engineering |
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| Checksum OK | Construction |
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With some occaisonal help from Bluefish.