EFcalc - Event/Fault Tree Calculator |
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The following example problem is used in the popular SAPHIRE code, used by many in the probabilistic risk analysis field. The problem has two fault trees, shown below:
The problem has one event tree with only two top-level systems, ecs and ccs.
To compute this problem using EFcalc, the following input files are used (default values for demo.cal were used):
demo.bas -
tank 0.0 "RWST supply to the inject and cool systems"
dga 0.0 "Emergency diesel generator A"
dgb 0.0 "Emergency diesel generator B"
cmov1 0.0 "CCS suction isolation valve"
emov1 0.0 "ECS suction isolation valve"
ccva 0.0 "CCS Train A pump discharge check valve"
cmova 0.0 "CCS Train A pump discharge isolation valve"
cpumpa 0.0 "CCS Train A motor-driven pump"
ccvb 0.0 "CCS Train B pump discharge check valve"
cmovb 0.0 "CCS Train B pump discharge isolation valve"
cpumpb 0.0 "CCS Train B motor-driven pump"
ecva 0.0 "ECS Train A pump discharge check valve"
emova 0.0 "ECS Train A pump discharge isolation valve"
epumpa 0.0 "ECS Train A motor-driven pump"
ecvb 0.0 "ECS Train B pump discharge check valve"
emovb 0.0 "ECS Train B pump discharge isolation valve"
epumpb 0.0 "ECS Train B motor-driven pump"
demo.equ
ccs or ccssupply ccstrains "CCS Fails to Spray Water in Cntnmnt"
ccssupply or tank cmov1fails "No Water to the Pump Trains"
cmov1fails or cmov1 dgb "C-MOV-1 Fails to Open"
ccstrains and ccsa ccsb "Both Pump Trains Fail to Inject"
ccsa or ccva cmova cpumpa dga "CCS Train A Fails to Supply Flow"
ccsb or ccvb cmovb cpumpb dgb "CCS Train B Fails to Supply Flow"
ecs or ecssupply ecstrains "ECS Fails to Inj Wat in the R Ves"
ecssupply or tank emov1fails "No Water to the Pump Trains"
emov1fails or dga emov1 "E-MOV-1 Fails to Open"
ecstrains and ecsa ecsb "Both Pump Trains Fail to Inject"
ecsa or ecva emova epumpa dga "ECS Train A Fails to Inject"
ecsb or ecvb emovb epumpb dgb "ECS Train B Fails to Inject"
demo.etr
2
ecs 0.0 0.0
ccs 0.0 0.0
3 eventtree "The SAPHIRE Event Tree"
con1 -ecs
con2 ecs -ccs
con3 ecs ccs
demo.con
con1 "All Right"
con2 "Large Release"
con3 "Small Release"
demo.dmg
tank 0.0000001
dga 0.02
dgb 0.02
cmov1 0.001
emov1 0.001
ccva 0.0001
cmova 0.005
cpumpa 0.003
ccvb 0.0001
cmovb 0.005
cpumpb 0.003
ecva 0.0001
emova 0.005
epumpa 0.003
ecvb 0.0001
emovb 0.005
epumpb 0.003
Running EFcalc produce the following *.ans file:
1 Number of Event Trees
3 Sequence probabilities and uncertainties
0.978799 0.000000
0.020444 0.000000
0.000757 0.000000
3 Consequence probabilities and uncertainties
1 0.978799 0.000000
2 0.020444 0.000000
3 0.000757 0.000000
2 Event tree branch probabilities
3 2 0.0357
3 1 0.0212
cmov1fails 0.020980 0.000000
ccsa 0.027923 0.000000
ccsb 0.027923 0.000000
emov1fails 0.020980 0.000000
ecsa 0.027923 0.000000
ecsb 0.027923 0.000000
ccssupply 0.020980 0.000000
ccstrains 0.000780 0.000000
ecssupply 0.020980 0.000000
ecstrains 0.000780 0.000000
ccs 0.021201 0.000000
ecs 0.021201 0.000000
Note that this example only had only 3 common components, so the direct method of computation was used. This is the reason that the uncertainty for every calculated value is zero. Had the Monte Carlo approach been used, these uncertainties would have had values.
The report file, demo.rpt, produced by the EFcalc run looks like the following:
---------------------------------------------------------------------
Reading Main Input Files...
Reading basic event definitions from demo.bas
Reading gate equations from demo.equ
Reading event tree sequences from demo.etr
Reading calculation parameters from demo.cal
Reading consequence names from demo.con
Reading failure probabilities from demo.dmg
---------------------------------------------------------------------
Setting up the basic event probabilities...
Resetting all basic event probabilities to zero.
---------------------------------------------------------------------
Manipulating and Checking Data...
Setting consquences for each event tree
Checking calculational parameters
Checking basic event probabilities
Checking simple failure probabilities of top level gates
Checking gate (12) and basic event (17) usage
Number of basic events: 17
Number of events not used: 0
Number of events used once: 14
Number of common events: 3
Number of house events: 0
Number of commons (exc. house): 3
Problem Overview
Number of basic events 17
Number of equations 12
Number of top-level systems 2
Number of event trees 1
Number of consequences 3
---------------------------------------------------------------------
Solving the Event Tree/Fault Tree System...
Method of Solution: Brute force on common variables
Determining event tree branch probabilities
---------------------------------------------------------------------
Event Tree Event Tree 1
seq 1 1 0.978799 0.000000
seq 2 2 0.020444 0.000000
seq 3 3 0.000757 0.000000
total 1.000000
con 1 con1 0.978799 0.000000
con 2 con2 0.020444 0.000000
con 3 con3 0.000757 0.000000
total 1.000000
With different failure probabilities in the demo.dmg file, different results are obtained:
| name | Standard | Case 2 | Case 3 | |
|---|---|---|---|---|
| tank | 10-7 | 10-6 | 10-5 | |
| dga | 0.02 | 0.2 | 0.2 | |
| dgb | 0.02 | 0.2 | 0.2 | |
| cmov1 | 0.001 | 0.01 | 0.1 | |
| emov1 | 0.001 | 0.01 | 0.1 | |
| ccva | 0.0001 | 0.001 | 0.01 | |
| cmova | 0.005 | 0.05 | 0.5 | |
| cpumpa | 0.003 | 0.03 | 0.3 | |
| ccvb | 0.0001 | 0.001 | 0.01 | |
| cmovb | 0.005 | 0.05 | 0.5 | |
| cpumpb | 0.003 | 0.03 | 0.3 | |
| ecva | 0.0001 | 0.001 | 0.01 | |
| emova | 0.005 | 0.05 | 0.5 | |
| epumpa | 0.003 | 0.03 | 0.3 | |
| ecvb | 0.0001 | 0.001 | 0.01 | |
| emovb | 0.005 | 0.05 | 0.5 | |
| epumpb | 0.003 | 0.03 | 0.3 | |
| Results | Standard | Case 2 | Case 3 | |
| Seq 1 | /ecs | 0.9788 | 0.7754 | 0.3799 |
| Seq 2 | ecs /ccs | 0.0204 | 0.1561 | 0.2097 |
| Seq 3 | ecs ccs | 0.0008 | 0.0685 | 0.4104 |
Oak Ridge National Laboratory, 2004