Approach: Fault tree analysis
E0 – Top event: operational
failure or life-safety
failure (two trees)
E0
Ei – Basic event: damage of
individual equipment
E23
“or” - gate
“and” - gate
E1
E2
E3
(E0 occurs) if and only if (E1occurs OR both E2 and E3 occur)
Fault tree analysis (continued)
Mathematical equivalent of gates (independent events):
E0
O
P (O)  1   1  P ( I i ) 
N
i 1
E23
I1
IN
O
N
E1
E2
P (O )   PI i 
E3
i 1
I1
IN
For the example fault tree:
PE0 | EDP   1  1  PE1 | EDP 1  PE2 | EDP PE3 | EDP 
Decision variables and top-event definitions
Events of interest and proposed Decision Variables (DV):


Life safety failure: DVLS=P(LSF | T), where LSF is
 Occurrence of a life-threatening event, T = planning period
(alternatively: DVLS=P(LSF|IM))
Operational Failure: DVO=P(OF | T) or P(OF | IM), where OF is


Repair or replacement time of critical equipment exceeds
some threshold value DT0.
Research products lost and the time to repeat the study is
greater than some threshold value RT0.
Required performance level is specified by DVLS, DVO, DT0, RT0
Fault tree illustration for an LSA laboratory
Operational Failure
Subject Die
Env. Failure
Temp. Changes
Critical Equipment Failure
Trauma
Microscope
is broken
Data Lost
Data storage
device is broken
Containment Failure
Basic event
(Damage State)
Hazmat Release
Tube is broken
To be refined upon consulting Comerio’s database, Comerio and LSA occupants
Expected Results
Result of calculation of
DV=P(E0 | EDP)


1.0
1.0
DV
DV
0.0
x1
x2
x3
Result of calculation of
DV=P(E0 | IM) by applying
theorem of total probability
0.0
x1
IM
N
Each point corresponds to a
particular value of the vector of
EDP at the given level of IM
x2

x3
IM

PE0 | IM  xi    P E0 | EDP  V j P EDP  V
j 1
Where N – is number of simulations at the level
IM=xi, and the right part probabilities are all
conditioned on IM= xi
j

What we would like from structure modeler (Mosalam)
SIM #
GM ID
Files in formats: CSV, MDB, XLS.
EDP ID
EDP Value
What we would like from fragility testers
Fragility Parameters
Assembly ID
Assembly Name
DS
Files in formats: CSV, MDB, XLS.
EDP Type
P1 (e.g. )
P2 (e.g.  )
Expected Results (Simulation Technique)
Result of simulation of E0| EDP,
using generated El events

P(E0 | EDP), using generated
El events

1.0
E0
DV
n1
n2
m1
x1

m2 n3 m3
x2
x3
0.0
IM
Generate basic event Ei according
to distribution P(El | EDP = Vk)
Follow Boolean logic of the fault tree
to know if E0 has happened
 Repeat for all Vk , and get ni, mi for
each level of excitation IM= xi

x1
x2
PE0 | IM  xi  
x3
IM
mi
mi  ni 
Where mi – is number of simulations
when E0 has happened, and ni – is
number of simulations when E0 has not
happened