P
E
E
R
UC Science Building Testbed
Meeting 16 Sep 2002
Porter, Beck, & Shaikhutdinov
Methodology Overview
PEER PBEE ANALYSIS METHODOLOGY
facility def.
Hazard
analysis
Structural
analysis
Damage
analysis
Loss
analysis
hazard model
struct’l model
fragility fns
loss model
p[IM|O,D]
p[EDP|IM]
p[DM|EDP]
p[DV|DM]
site hazard
structural
response
damage
performance
decision
p[DM]
p[DV]
O, D OK?
O, D
p[IM]
O: Location
D: Design
IM: intensity
measure
EDP: eng'ing
demand param.
DM: damage
measure
DV: decision
variable
"What are my
options for the
facility location
and design?"
"How likely is an
event of
intensity IM, for
this location and
design?"
"What
engineering
demands (force,
deformation,
etc.) will this
facility
experience?"
"What physical
damage will
facility
experience?"
"What loss
(economic,
casualty, etc.)
will this facility
experience?"
p[EDP]
2
"Are the
location and
design
acceptable?"
Decision Basis
•
•
Applies to an operational unit for a given planning
period T, location O, and design D
Probability of operational failure
–
•
Probability of life-safety failure
–
•
•
Operational failure occurs if any component that is
critical for operations fails
Life-safety failure occurs if any component that is
critical for operations fails
Probability distribution of repair cost
Probability distribution of repair duration
3
Decision Variables
• Applies to an operational unit
• DVO: binary RV for operational state
•
•
•
•
= 1  operational failure
DVL: binary RV for life-safety state
= 1  life-safety failure
CR = repair cost, a scalar RV
DR = repair duration, a scalar RV
Goal:
P[DVO=1 | T, O, D]
P[DVL=1 | T, O, D]
FCR|T,O,D(cr|t,o,d) – a CDF of repair cost given T,O,D
FDR|T,O,D(dr|t,o,d)
4
Damage Measures
•
•
Applies to a component
DMR,i: binary RV for component i requiring repair or replacement
–
–
DMR,i = 1  component requires repair or replacement
Assume repair or replacement required if:
•
•
•
•
DMO,i: binary RV for operation-critical-component i operational state
–
–
DMO,i = 1  operational failure of component
Operational failure means
•
•
•
Overturns (including sliding off bench or shelf)
Impact sufficient to damage items
Stored in equipment that overturns
Operation-critical equipment or specimen & DMR,i = 1
Door of refrigerator containing operation-critical specimens opens, or
DML,i: binary RV indicating component i life-safety state
–
–
DML,i = 1  life-safety failure of component
Life-safety failure means
•
•
•
•
Life-safety hazard = “D” & overturns (O/T) or
Chemical hazard ≠ “N” & overturns or
Unrestrained weighty object & achieves momentum sufficient to cause trauma
Unrestrained weighty object & displacement is great enough to block egress
5
DV|DM for Equipment
• DVO = maxi(DMO,i)
• DVL = maxi(DML,i)
• CR = ΣDMR,iCR,i
– CR,i = uncertain repair or replacement cost, equipment
component i. The equation is different for construction.
• DR = Max(DMR,iDR,I)
– DR,i = uncertain repair or replacement time, equipment
component i. The equation is different for construction.
6
DV|DM for Construction Cost
• CR = (1 + CO&P)SjSdNj,dCj,d
CR = repair cost
CO&P = overhead & profit, ~U(0.15, 0.20)
j = index of assembly type
d = index of damage state
Nj,d = number of assemblies of type j in state d
Cj,d = unit cost to restore assemblies of type j
from state d, ~LN(mCj,d, bCj,d)
7
DV|DM for Construction Duration
• TR,m = T0 + SjSdTj,dNj,d/nj,d + StNtTt
TR,m = time to restore operational unit m
T0 = design, contracting, and mobilization time
Tj,d = time for one crew to restore one unit of assembly type j from
state d, weeks.
nj,d = number of crews available
Nt = number of changes of trade
Tt = change-of-trade delay, weeks.
• Slow repair: high T0, low nj,d, high Tt, operational units
restored in series (trades move from one unit to next)
• Fast repair: low T0, high nj,d, low Tt, operational units
restored in parallel
8
Assembly DM|EDP Fragility Functions
• Fragility function gives the probability that an
undesirable event (“failure”) occurs given input
excitation (engineering demand parameter)
• Possible equipment EDP
– Peak diaphragm acceleration (PDA) or
– Peak diaphragm velocity (PDV) or
– Both
• Need P[DML,i|EDPi], P[DMO,i|EDPi]
– May depend on P[O/T|EDP], P[URD|EDP] or P[O/T or
URD|EDP]
9
Sample Lab
Lab
Count
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
Cande
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
24
Equipt
Key
J
K
B
G
L
M
N
E
P
WS-1-2
WS-3
WS-4
WB-2
C
B
H
I
K
M
N
Equipt
Name
Incubator
Freezer
Refrigerator
Refrigerator
Centrifuge
Refrigerator
Refrigerator
Fume Hood
Fume Hood
Open Shelving
Open Shelving
Open Shelving
Work Bench
Incubator
Low Temp. Incubator
Incubator
CPU
Monitor
CPU
Monitor
Mfg
Percival
Coldspot
Philco
Kenmore
Du Pont…
Kenmore
Fisher Sci
VWR Sci
Precision
Silicon Gr
Silicon Gr
Silicon Gr
Silicon Gr
Life Safety
Haz.
D
D
D
D
D
D
D
C
C
A/SL
A/SL
A/SL
A
C
B
B
B
B
B
B
Ct(“D”) = 8
Import.
Chem Haz.
Y
Y
N
N
N
N
N
N
N
N
N
N
N
Y
Y
Y
Y
Y
Y
Y
Ct(“Y”) = 9
N
N
N
N
N
N
N
CH/A
CH/A
CH/A
CH/A
CH/A
CH/A
N
N
N
N
N
N
N
Ct(“CH/A”) = 9
Makris will provide fragilities from top of list through fume
10hoods by 1 Dec.
Hutchison will provide others. Draft fragilities to be delivered by early to mid-December
From Overturning and Unrestrained Displacement to
Life-Safety and Operational Failure
Life Safety Haz D
Import. Y
Chem Haz
Weighty
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
11
p[DML,i=1|EDP]
p[DMO,i=1|EDP]
0
P[URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
0
P[URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
P[O/T|EDP]
P[O/T or URD|EDP]
0
0
0
0
P[O/T|EDP]
P[O/T|EDP]
P[O/T|EDP]
P[O/T|EDP]
0
0
0
0
P[O/T|EDP]
P[O/T|EDP]
P[O/T|EDP]
P[O/T|EDP]