Use of Boolean Logic and Probabilistic Analysis in work
During my YINI placement I have been working in the Safety Case Team for Hinkley Point B and
Hunterston B nuclear power stations at British Energy – part of EDF Energy, the owner and operator of eight
nuclear power stations in the UK.
When designing and operating a nuclear power station, safety is a top priority. Modern power stations
operate with the help of Probabilistic Safety Analysis (PSA). This enables the frequency of radiological
releases to be calculated, and helps the Company keep the frequency of these events as low as reasonably
practicable (ALARP), with a target of less than a 1 in a million chance of a significant release per year.
The frequency of radiological releases is calculated using a PSA model on a computer.
This program enables us to create fault trees using Boolean Logic. Once completed, a model will have
hundreds of fault trees and event trees, and the probability of every conceivable hazard and its consequence
can be calculated in minutes.
The diagram below illustrates a simple fault tree with arbitrary values assigned.
Probability of Emergency feed
system failing
= 0.1702
Emergency feed system fails
OR
0.01
0.0602
Basic Event
(e.g. a pipe leak
or electrical
failure)
0.1
No feed from pumps
Valve 2
Fails
OR
Common
Cause fault
0.0102
0.05
Probabilities
multiply at
AND gates
Both pump trains fail
Valve 1 Fails
to open
AND
0.101
0.101
Probabilities add
at OR gates
No feed from train A
No feed from train B
OR
OR
0.1
0.001
0.1
0.001
Probability
of event
occurring
(ie. probability
of plant item
failing)
Pump A
fails
Valve A
fails
Pump B
fails
Valve B
fails
(Note that real probability values are much lower)
This is a simple example of one fault tree. This fault tree would then connect to other fault trees and event
trees in the model relating to different parts of the plant. Fault trees are particularly useful when planning
maintenance. Suppose Pump B had to be taken offline for maintenance. One could use the PSA model to
work out the probability of the emergency feed system failing if pump B is unavailable - see diagram below.
Benjamin Brocklehurst
MEI Mathematics at work competition 2010
Probability of Emergency feed
system failing
= 0.261
Emergency feed system fails
OR
0.151
0.01
0.1
Increase ratio
= 0.261/0.1702
= 1.533
No feed from pumps
Valve 2
Fails
OR
Common
Cause fault
0.101
0.05
Both pump trains fail
Valve 1 fails
to open
AND
FAILED
0.101
No feed from train A
No feed from train B
OR
OR
0.1
Pump A
fails
0.001
UNAV
Valve A
fails
Pump B
fails
0.001
Valve B
fails
By repeating this process
on the full PSA model, it
is possible to test the
contribution each plant
item has in reducing the
frequency of events.
The graph shows the %
increase in events caused
by
unavailability
of
combinations of plant
items.
As shown in the graph,
the frequency of events
increases by over 2000%
if plant items in case
number 21 are made
unavailable. Therefore the
operating rules would
forbid the operators from
entering this condition as
the frequency of events is
no longer ALARP.
Benjamin Brocklehurst
% in c re a s e in e v e n t fre q u e n c y
Making pump B unavailable does not fail the whole system because pump A is still functioning normally.
However, the probability of the system failing has increased by a factor of 1.533 as only one pump is now
available to feed the system. Therefore the operators would wish to carry out the maintenance of pump B as
quickly as possible in order to keep the probability of the system failing ALARP.
2000.0%
1500.0%
1000.0%
500.0%
0.0%
1
4
8 11 14 17 20 23 26 29 32 35 38 41 44 47 50 53 56 59 62
Case No.
MEI Mathematics at work competition 2010