The business of PHM : An “Actuarial Engineering ... - PHM Society

GE
Energy
The business of PHM :
An “Actuarial Engineering”
perspective
Annual Conference of the Prognostics & Health
Management Society 2010
October 10-14, 2010
Portland, Oregon
Sameer Vittal, PhD
GE Energy – Advanced Technology Operations

GE Energy
Employees: 82,000
• „09 revenue: $37.1B
• Operating in 140 countries
Power & Water
Energy Services
Oil & Gas
• Power generation
• Renewables
• Gas Engines
• Nuclear
• Gasification
• Water treatment
• Process chemicals
• Contractual agreements
• Smart Grid
• Field services
• Parts and repairs
• Optimization
technologies
• Plant management
• Drilling/production for …
land, offshore, subsea
• LNG and pipelines
• Refining/petrochemical
• Industrial power gen
• Complete lifecycle
services
(c) General Electric Company - 2010
2
10/12/2010

PHM Serves Diverse Technologies
Gas
Wind
Nuclear
Solar
Smart Grid
Biomass
Pipeline
Integrity
Water
Technologies
Cleaner Coal
Oil & Gas
(c) General Electric Company - 2010
3
10/12/2010

Life Management Evolution
1930-1960 1960-1985
1985-2000 2000-2005
1 st Generation
Corrective
Maintenance
2 nd Generation
Preventive
Maintenance
3 rd Generation
Predictive
Maintenance
• Fix when broken
• Very popular
• All life consumed
• Scheduled
• High forced outage
replacement
costs
• Low forced outage
• Hard to predict
costs / risk
• Poor availability
• Higher scheduled
outage costs
• Wasteful
2006+
4 th Generation
Intelligent Engine
Health Management
• Integrate controls with CBM/PHM
• Optimize asset usage
Reliability
Centered
Maintenance
(RCM)
Condition
Based
Maintenance
(CBM)
Prognostics
Health
Monitoring
(PHM)
• Interval from
reliability bathtub
curve
• E.g. B1 life
• Useful for
unobserved risks
• Physics/Empirical
Damage
accumulation
• Update model
w/inspection data
• Risk-Based
Inspection (RBI)
• Real-time
• M&D data based
• Fault / Anomaly
detection &
isolation (FDI)
• Prognostics &
Diagnostics
Optimal part life usage, improved reliability, availability
maintainability & safety (RAMS), reduced O&M costs
(c) General Electric Company - 2010
4
10/12/2010

The business of PHM …
Prevent catastrophic
failures & forced outages
Part Life Management
High-Value Assets
Performance Optimization
Sensors & Data Collection
Signal Processing and Analytics
Better designs & retrofits
Operational Risk Mgmt
Intelligent Business Processes, New Products & Services
Sensors & Analytics provide intelligence and differentiated business processes that allow GE to
develop new products & services … and generate value over the life of the asset
(c) General Electric Company - 2010
5

New Roles for PHM &
Asset Management
New Business Models, Products
• Extended warranties
• Long term service agreements
• Operation & Maintenance Agreements
• New types of assets .. E.g. Renewable energy
Technology & Reliability, Risk
• Costs of collecting, storing and analyzing data continues to
fall .. moving from terabyte to petabyte level databases
• Reliability & Risk Management needs to operate in a realtime
24/7 environment
(c) General Electric Company - 2010
6

Beta
Unreliability, F(t)
99.00
90.00
50.00
10.00
5.00
1.00
0.50
0.10
0.05
0.01
5.00
4.00
3.00
2.00
1.00
0
Gearbox Failures - Reliability Vs Ledger Data
1000.00 10000.00
100000.00
Hours
Gearbox Failures - Reliability Vs Ledger Data
47740.00 104462.00 161184.00 217906.00 274628.00 331350.00
Hours
Weibull
LedgerData_2008
W2 MLE - SRM MED
F=70 / S=4014
ReliabilityData
W2 MLE - SRM MED
F=53 / S=4014
CB[FM]@95.00%
2-Sided-B [T1]
Sameer Vittal
GE Energy
2/8/2009 15:05
Weibull
LedgerData_2008
W2 MLE - SRM MED
F=70 / S=4014
ReliabilityData
W2 MLE - SRM MED
F=53 / S=4014
Level 1 : 95%
Level 2 : 90%
Sameer Vittal
GE Energy
2/8/2009 15:08
Unreliability, F(t)
99.90
90.00
50.00
10.00
5.00
1.00
0.50
0.10
Probability - Weibull
1000.00 10000.00 100000.00
1000000.00
Time, (t)
W2 MLE - SRM MED
F=129 / S=0
Labor
W5 MLE - SRM MED
F=181 / S=0
Other
W2 MLE - SRM MED
F=29 / S=0
Parts
W5 MLE - SRM MED
F=174 / S=0
SalesTax
W5 MLE - SRM MED
F=15 / S=0
Unreliability, F(t)
99.90
90.00
50.00
10.00
5.00
1.00
0.50
0.10
Total Costs
100.00 1000.00 10000.00 100000.00 1000000.00 1.00E+7
Costs, $
Weibull
TotalCost
W5 MLE - SRM MED
F=204 / S=0
CB[FM]@95.00%
2-Sided-B [T1]
Avg Cost Per Event, $
CBM Alarms/Anomalies
Per Turbine
Assessing & Communicating Value in PHM
Business Value & Risk assessed
using stochastic risk management
processes
• Value & Risk models help define
the product
• Scenario-Based & Probabilistic
• Leverage best practices from
actuarial science & energy risk
Weibull‟s &
Maintenance
Factors
$45,000,000
$40,000,000
$35,000,000
$30,000,000
$25,000,000
$20,000,000
$15,000,000
$10,000,000
$5,000,000
$-
$(5,000,000)
$(10,000,000)
Financials
(Parts/Labor/
Logistics)
Gearbox Failure Costs, 2006-2008
(Major Categories Like Parts, Crane, Labor & recoveries)
Sum of
Parts
Sum of
Crane
Sum of
Labor
Major Cost Category
Sum of
Total
Sum of
Recoveries
Weibull
Crane
Winergy
Unknown
Rexroth
Moventas
GETS
Eichkoff
CBM
Capability
Detection
Probability
Downtime
Scenario
Simulation
Loss Models
$250,000
$200,000
$150,000
$100,000
$50,000
$-
Deal Financials &
Portfolio Analytics
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.0
$(50,000)
Expected Drivetrain Events/CBM Alarms Over 2o Yrs
MainBrg
Generator
Gearbox
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
$81,377
Operating Time (Years)
Average Gearbox Failure Cost Breakdown Per Event
(Ledger Data, 2006-2008)
$26,766
$4,488
$116,253
$(31,442)
$2,304
CRANE LABOR OTHER PARTS RECOVERIES SALES
TAX
$199,745
TOTALS
Asset Health Usage &
Management System
Advanced
Reporting
Anomaly
Detection
Life
Management
Reasoners
Data Fusion
Optimizers
SMART SERVICES
Spare Parts/Pools
Logistics & Supply Chain
Risk-Based Inspection
Maintenance Workscope
Repair Optimization
Availability Guarantees
Performance Guarantees
Business Interruption Risk
BUSINESS CASE & VALUE PROPOSITION DRIVES PHM SYSTEM ARCHITECTURE
(c) General Electric Company - 2010
7

Frequency
Unreliability
What Is Actuarial Science ? Why is it relevant ?
• Provide commercial, financial and risk
management advice on the management of
assets & liabilities, especially for long time
horizons
• Actuaries are the DNA of the insurance industry
• “..for most actuaries, the role involves making
financial sense of the future” (Institute of
Actuaries, UK)
• Education is university-based or examinationbased.
Heavily regulated, global profession with
professional standing
• Practice areas are Life, Health, Property &
Casualty, Pensions, Benefits and Investments
(usually of insurers)
• “Identify and analyze the financial consequences
of events involving risk and uncertainty” –
historically use past observation and wisdom to
construct, validate and apply models
99.90
90.00
50.00
10.00
5.00
1.00
0.50
0.10
GLL-Weibull Model
0.01 0.10 1.00
10.00
Time
Beta=1.4434, Alpha(0)=-0.1885, Alpha(1)=0.0013, Alpha(2)=3.7633E-5
Distribution Curve for Creep or Fatigue
Log (time) or Log (cycles)
GLL/Weib
Data 1
552 / 10585
F=298 | S=0
CL: 95.00%
2 Sided-B
Time [T1]
Sameer Vittal
GEPS Reliability
9/14/2002 17:30
(c) General Electric Company - 2010
8

Actuarial Skills -> Engineering Asset Management
Risk Measurement Risk Models / Valuation Risk Control
• Modeling rare events / extreme
value statistics .. Wide range of
distributions (100+ used !)
• Model and parameter
uncertainty .. Goodness of fit
(LL, BIC, AIC, H-Q)
• Understanding correlations
(structural, statistical)
• Model updating and synthesis
(credibility theory)
• Catastrophe risk analysis
(models, methods)
• Ruin theory applied to
engineering systems
• Financial value of risk, Loss Models
(Frequency/Severity)
• Portfolio-based approach to
asset health management
• Risk Concentration
• Risk Diversification
• Correlations .. Copulas
• Metrics … VaR, CTE, RAROC
• Regression Vs. simulation,
scenario based valuation
• New service products / revenue
streams built around the physical
asset (from transactional to
annuity-type model)
• Loss reserving (methods,
tools, standards) and Pricing
– the risks you assume
• Identify, exclude hazards that
cannot be controlled (terms &
conditions)
• Integrate asset life
management into an
Enterprise Risk
Management framework
(operational risk)
(c) General Electric Company - 2010
9

Unreliability, F(t)
L if e
Beta
Basics …Classical Life Data Analysis
Typical Part Life Data - For
illustrative purposes only
Old
Insp.
(Hrs)
New
Insp.
(Hrs)
Usage
Factor
(X1)
Parts
Fail
Parts
OK
1000 3000 2400 4 88
2000 4000 2250 3 89
9000 20000 2350 3 89
12000 20000 2100 4 88
15000 25000 2050 7 85
18000 25000 2150 8 84
2000 6000 2200 1 91
3000 12000 2200 2 90
6000 18000 2100 6 86
6000 20000 2150 8 84
Other analysis types include,
• Non Parametric Methods
• Parametric with Physics-based Aging
• Logistic Regression
• Nonlinear Regression
• Probit Analysis
• Generalized Poisson Process Models, etc
99.00
90.00
50.00
10.00
5.00
1.00
0.50
0.10
4
Standard Weibull
Probability - Weibull
Distribution
3
500000. 000
x 88
x 89
x 91
2
1000.00 10000.00
100000.00
Time, (t)
10000. 000
6
x 90
8 34 7 8
x 86
x 84 89 88
x 85 84
Beta= 2. 9901; Alpha(0)= -85. 4726; Alpha(1)= 0. 0245
Weibull
Data 1
3.00
W2 MLE - RRM MED
F=46 / S=874
CB[FM]@95.00%
2-Sided-B [T1] 2.60
2.20
1.80
1.40
Weibull Proportional Hazards Model (Varying Usage Conditions)
Weibull Proportional Hazards
1.00
Risk = f(Age, Usage)
1000. 000
2000. 2120. 000 2240. 000 2360. 000 2480. 000
000 2600. 000
Usage Parameter
Weibull Parameters - Joint
Confidence Interval
Weibull Parameters - Joint Confidence Interval
Life
CB@ 90% 2-Sided
57620.00 81938.00 106256.00 Data 1 130574.00 154892.00 179210.00
Proportional Hazards
W eibull Eta
10
F=46 | S= 874
Eta Line
Top CB Eta
Bottom CB Eta
2050
Eta Point
Imposed Pdf
2100
Eta Point
Imposed Pdf
2150
Eta Point
Imposed Pdf
2200
Eta Point
Imposed Pdf
2250
Eta Point
Imposed Pdf
2350
Eta Point
Imposed Pdf
2400
Eta Point
Imposed Pdf
Weibull
Data 1
W2 MLE - RRM MED
F=46 / S=874
: 95%
: 90%
: 85%
: 80%
(c) General Electric Company - 2010
10

Availability, A(t)
From part to system risk / reliability
Part Failure and Repair Distributions, and
other variables as needed (repairs,
inspections, logistics, spares, costs, etc)
Failure Distribution Repair Distribution
Component Eta (hr) Beta Mu (hr) Sigma
FuelTank 200000 1.5 168 20
Engine_1 75000 2.5 336 48
Engine_2 75000 2.5 336 49
Engine_3 75000 2.5 336 50
Generator_1 100000 4.5 250 120
Generator_2 100000 4.5 250 120
Generator_3 100000 4.5 250 120
Transformer 85000 3.0 1000 250
Weibull
Normal
Data for illustrative purposes only
Reliability Block Diagrams are often used to predict
component impact on overall system reliability,
availability, safety and life cycle costs
Fuel_Tank
Engine_1
Generator_1
Engine_2 Generator_2 Junction Transformer
Engine_3
Generator_3
Point Availability vs Time
Other system reliability methods include,
• General Discrete Event simulation
• Fault Tree Analysis
• Markov & Semi-Markov Models
• Stochastic Petri Nets
• Queuing Models
• Bayesian Networks (Adapted)
16810.025
13448.020
10086.015
6724.010
1.000
0.800
Block Downtime
0.600
0.400
0.200
SAMEER VITTAL
Engine_3 GENERAL ELECTRIC
9/19/2008
10:01:01 PM
0.000
0.000 35040.000 70080.000 105120.000 140160.000 175200.000
Time, (t)
RS DECI
100%
50%
0%
8 Item(s)
Transformer
Generator_3
Generator_2
Generator_1
Fuel_Tank
Engine_2
Availability
Diagram1
Point Availability Line
Block Up/Down
State
Operating Time
Time Under Repair
3362.005
Engine_1
0.000
TransformerEngine_3 Engine_1 Generator_2Generator_3 Engine_2 Fuel_Tank Generator_1
SAMEER VITTAL
GENERAL ELECTRIC
9/19/2008
10:04:04 PM
SAMEER VITTAL
System
GENERAL ELECTRIC
9/19/2008
10:02:04 PM
0.000 35040.000 70080.000 105120.000 140160.000 175200.000
E.g. Component downtime, availability & operational status
Time, (t)
(c) General Electric Company - 2010
11

Frequency
0
57
113
170
226
283
339
396
453
509
566
622
679
735
792
Frequency
0
57
113
170
226
283
339
396
453
509
566
622
679
735
792
Frequency
0
57
113
170
226
283
339
396
453
509
566
622
679
735
792
Quantifying the Impact of Anomaly Detectors
Consider a simple example where we have a system with an onboard sensor / anomaly detection algorithm
that detects failures in advance with some probability of detection (PoD). If failure indications are detected
early on, associated risks, downtime durations & failure costs are typically much lower
Simulation-based trade studies can be used to optimize the sensor suite (PoD, false alarm rate, time to
detect, etc) with the asset being monitored. This significantly improves reliability, reduces outage durations
and reduces overall system operational risk.
250
200
150
100
50
0
Failure
System OK
Downtime Duration Histogram, PoD = 50%
(from 5000 Monte Carlo trials)
Downtime Histogram
PoD = 0%
Detected,
“Planned”
Event
Not detection
“Unplanned”
Event
600
500
400
300
200
100
0
Assumptions / Input
Key Statistics
Event Type Distribution Mean StDev
Time to Failure (hr) Weibull 22181.6 9491.7
Planned Downtime (hr) Lognormal 48 18
Unplanned Downtime (hr) Lognormal 480 75
Data & results for illustrative purposes only
Downtime Duration Histogram, PoD = 50%
(from 5000 Monte Carlo trials)
Downtime Histogram
PoD = 50%
1200
1000
800
600
400
200
0
Downtime Duration Histogram, PoD = 50%
(from 5000 Monte Carlo trials)
Downtime Histogram
PoD =100%
Downtime (hrs)
Downtime (hrs)
Downtime (hrs)
(c) General Electric Company - 2010
12

Unreliability, F(t)
Beta
Case Study 1 : From Weibull‟s to Loss Models
• We show how life data analysis can be combined with a PHM metric (E.g. Probability of
Detection) to estimate a distribution of losses (costs)
• Impact of model parameter uncertainty on “tail” risks .. Concept of VaR, TVaR, etc.
Step 1 : Collect failure (“F”) &
suspensions / right-censored “S” data
Type
Failure
Time Type
Failure
Time
S 0.824 F 4.900
S 1.046 S 4.999
S 1.416 F 5.271
F 1.428 F 5.760
S 1.801 F 5.772
S 2.091 F 5.896
S 2.419 F 6.093
F 2.835 S 6.201
S 2.905 F 6.242
F 3.038 S 6.271
S 3.182 F 7.495
S 3.188 S 7.495
F 3.394 F 8.282
F 3.602 F 8.527
F 3.607 F 9.181
F 3.635 F 9.349
F 3.670 F 9.379
F 3.689 F 10.142
F 4.441 F 11.303
F 4.523 F 15.904
99.00
90.00
50.00
10.00
Note: This example is for illustrative purposes only
(c) General Electric Company - 2010
5.00
1.00
Step 2 : Fit a standard survival model (E.g. Weibull)
and estimate parameter uncertainties
Probability - Weibull
1.00 10.00
100.00
Time, (t)
3.40
2.92
2.44
1.96
1.48
1.00
Value
W2 MLE - SRM MED
F=27 / S=13
CB[FM]@95.00%
2-Sided-B [T1]
Sameer Vittal
General Electric - Energy
10/6/2010 13:32
Lower
95% CI
5.00 6.00 7.00 8.00 9.00 10.00
Eta
Upper
95% CI
Eta = Weibull 7.5693 6.3807 8.9793
Data 1
Beta = 2.2462 1.7248 2.9252
Var-Eta Var-Beta
0.4352 Contour 0.0366 Plot
0.0366 0.0916
Weibull
Data 1
W2 MLE - SRM MED
F=27 / S=13
: 95%
: 90%
: 85%
Sameer Vittal
General Electric - Energy
10/6/2010 13:33
13

Case Study 1 : From Weibull‟s to Loss Models
Step 3 : A simple simulation
model in Excel (for demo
purpose only )
• Simple portfolio of 5 units ..
• All have identical Weibull life
distributions (same eta/beta)
• No parameter uncertainty
• Probability of Detection
assumed to be 65%
• If event is detected, lower
costs …if missed,
substantially higher cost
distributions
• Costs distributions (detected,
missed) are lognormal
• 20-Yr warranty assumed
• Run Monte Carlo trials .. use
any tool / VBA script
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Cost/Event Detect Miss
Eta (yr) 7.57 7.57 7.57 7.57 7.57 Dist LOGN LOGN
Beta 2.25 2.25 2.25 2.25 2.25 Mean $ 2,500 $ 25,000
Simulated Failure Time (Yrs) StDev $ 1,000 $ 10,000
TTF 1 8.7 4.9 5.7 9.5 4.4 CoV 0.4 0.4
TTF 2 12.4 13.4 11.1 11.9 15.9 Mu 7.244 9.547
TTF 3 18.5 19.7 16.9 20.8 22.5 Sigma 1.077 1.077
TTF 4 26.7 20.4 20.3 27.7 28.2
TTF 5 44.2 36.5 27.0 32.3 34.0 PoD 65% Avg-STD $ 1,576
Table that tracks events
Year Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Year Unit 1 Unit 2 Unit 3 Unit 4 Unit 5
1 0 0 0 0 0 1
2 0 0 0 0 0 2
3 0 0 0 0 0 3
4 0 0 0 0 0 4
5 0 detect 0 0 miss 5 $ 2,629
$ 25,543
6 0 0 miss 0 0 6 $ 878
7 0 0 0 0 0 7
8 0 0 0 0 0 8
9 detect 0 0 0 0 9 $ 1,630
10 0 0 0 detect 0 10 $ 10,489
11 0 0 0 0 0 11
12 0 0 detect miss 0 12 $ 242 $ 7,916
13 detect 0 0 0 0 13 $ 1,164
14 0 detect 0 0 0 14 $ 1,740
15 0 0 0 0 0 15
16 0 0 0 0 detect 16 $ 2,093
17 0 0 miss 0 0 17 $ 31,682
18 0 0 0 0 0 18
19 detect 0 0 0 0 19 $ 1,753
20 0 miss 0 0 0 20 $ 69,889
TOTAL $ 4,547 $ 74,258 $ 32,802 $ 18,405 $ 27,636
Screenshot of a typical MC trial
Note: This example is for illustrative purposes only
(c) General Electric Company - 2010
$/Yr $ 227 $ 3,713 $ 1,640 $ 920 $ 1,382
14

Case Study 1 : From Weibull‟s to Loss Models
Step 4 : A simple simulation
model in Excel (for demo
purpose only )
• Same portfolio of 5 units ..
• Unit Weibull‟s are not the same
• Eta/Beta pairs obtained from
Weibull covariance matrix ..
Assume they are bivariate
normal
• This scenario includes
parameter uncertainty
• Rest is same ..
• Run Monte Carlo trials ..
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Cost/Event Detect Miss
Eta (yr) 6.78 6.65 6.73 5.40 6.34 Dist LOGN LOGN
Beta 2.42 2.15 2.12 2.25 1.62 Mean $ 2,500 $ 25,000
Simulated Failure Time (Yrs) StDev $ 1,000 $ 10,000
TTF 1 5.5 3.3 9.4 3.9 5.7 CoV 0.400 0.400
TTF 2 8.5 11.5 15.7 6.2 13.5 Mu 7.244 9.547
TTF 3 13.8 14.9 18.4 11.7 20.8 Sigma 1.077 1.077
TTF 4 20.5 17.0 27.3 16.7 22.7
TTF 5 26.6 21.8 32.4 19.1 27.3 PoD 65% Avg/Yr/Unit $ 1,282
Table that tracks events
Year Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Year Unit 1 Unit 2 Unit 3 Unit 4 Unit 5
1 0 0 0 0 0 1
2 0 0 0 0 0 2
3 0 0 0 0 0 3
4 0 miss 0 miss 0 4 $ 27,043
$ 15,805
5 0 0 0 0 0 5
6 detect 0 0 0 detect 6 $ 4,966
$ 2,280
7 0 0 0 detect 0 7 $ 10,975
8 0 0 0 0 0 8
9 detect 0 0 0 0 9 $ 2,353
10 0 0 miss 0 0 10 $ 5,934
11 0 0 0 0 0 11
12 0 detect 0 detect 0 12 $ 376
$ 15,296
13 0 0 0 0 0 13
14 detect 0 0 0 detect 14 $ 620
$ 2,817
15 0 detect 0 0 0 15 $ 1,402
16 0 0 detect 0 0 16 $ 7,075
17 0 0 0 detect 0 17 $ 4,365
18 0 miss 0 0 0 18 $ 22,257
19 0 0 detect 0 0 19 $ 3,727
20 0 0 0 detect 0 20 $ 950
TOTAL $ 7,939 $ 51,078 $ 16,736 $ 47,391 $ 5,097
Screenshot of a typical MC trial
Note: This example is for illustrative purposes only
(c) General Electric Company - 2010
$/Yr $ 397 $ 2,554 $ 837 $ 2,370 $ 255
15

Case Study 1 : From Weibull‟s to Loss Models
Weibull with
Parameter
Uncertainty
Weibull
Parameters
Only
Statistic
Trials 5000 5000
Mean $1,451 $1,350
Median $1,228 $1,139
Std Deviation $983 $898
Variance $967,219 $806,465
Skewness 3.20 2.58
Kurtosis 29.99 18.82
CoV 0.6777 0.6653
Minimum $110 $94
Maximum $16,957 $12,962
Range Width $16,847 $12,868
Weibull with
Parameter
Uncertainty
Weibull
Parameters
Only
Percentiles
P0 $110 $94
P10 $554 $502
P20 $735 $676
P30 $886 $824
P40 $1,052 $973
P50 $1,228 $1,139
P60 $1,429 $1,334
P70 $1,658 $1,553
P80 $1,998 $1,881
P90 $2,604 $2,420
P100 $16,957 $12,962
Typical Metrics :
Value At Risk (VaR)
• Percentile of interest
(P95/P99) from loss model
• Depends on business risk
appetite
Conditional Tail Expectation
(CTE) or TVaR
Mean
EC
VaR95
CTE
• “Expected” value of losses in
tail (usually beyond the VaR
limit)
Risk-Adjusted Return On
Capital (RAROC)
• RAROC = Expected Return
VaR or EC
• Multiple uses in risk mgmt.
Note: This example is for illustrative purposes only
(c) General Electric Company - 2010
16

Case Study 1 : Observations
• Actuarial Methods .. Frequency/Severity or Discrete Event Simulationbased
… ARE applicable to engineering asset management
• Uncertainty matters !! (We all know this in PHM) .. But very critical for
risk as models get larger, more realistic .. Include economic variables,
shocks .. plus a lot of things that are hard to measure !!
• “Expected” values and “traditional” metrics .. RoI, NPV, IRR, are helpful,
but not enough.. The tail risk alone can wipe out a badly designed
contract / portfolio
• Communicate the value of PHM using the vocabulary of financial risk
management : VaR, CTE, RAROC, EC, etc. ..
• This is an EXTREMELY SIMPLE “made-up” example .. real projects
require both model & parameter uncertainties, asset correlations (E.g.
Copulas), systemic risk .. Contagion risk .. Risk attractors / diversifiers ...
beyond the scope of this presentation
(c) General Electric Company - 2010
17

Optimal Shell Thickness, in
$-
$5,000
$10,000
$15,000
$20,000
$25,000
$30,000
Loss Cumulative Density Function,
F(S)
$-
$1,000
$2,000
$3,000
$4,000
$5,000
$6,000
$7,000
$8,000
$9,000
$10,000
$11,000
$12,000
$13,000
$14,000
$15,000
$16,000
$17,000
$18,000
$19,000
$20,000
$21,000
$22,000
$23,000
$24,000
$25,000
Loss Probability Mass Function,
f(S)
Failure Probability, %
Failure Probability, %
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Case Study 2 : Probabilistic Design & PHM
Time-based FORM,
SORM, MF-FOSM, etc
Equivalent Weibull
Pressure Vessel - Time Dependent Failure Probability
Initial thickness = 0.38"
100%
90%
Limit State 1
80%
Limit State 2
System
70%
60%
H A L
A H
Pressure Tank
R
2 Limit States (ASME)
Design Variable : Shell Thickness
50%
40%
30%
20%
10%
0%
Time, years
Optimization
Variation of optimal shell thickness
with a warranty-based constraint
Actuarial Loss Model
Renewal Model
Pressure Vessel - Expected Renewals
Initial thickness = 0.38", warranty period is 25 years
0.42
100%
14%
2.5
0.41
0.40
0.39
0.38
Fs(x) = 0.90
Fs(x) = 0.80
Fs(x) = 0.70
Fs(x) = 0.60
90%
80%
70%
60%
50%
40%
Loss PDF
Loss CDF
12%
10%
8%
6%
2.3
2.0
1.8
1.5
1.3
Renewals
0.37
0.36
0.35
30%
20%
10%
0%
4%
2%
0%
1.0
0.8
0.5
0.3
0.34
Loss Amount, $
Figure 10 : Actuarial Loss Model for a 25 year warranty, design shell thickness of 0.38"
0.0
Time, years
Warranty loss amount, $
Reference : Vittal S. & Phillips, R., “Modeling and Optimization of Extended Warranties
Using Probabilistic Design”, RAMS2007, Orlando, FL (2007)
(c) General Electric Company - 2010
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PHM As Part of Risk Management
• PHM + Life-Extending Controls provide the “vital knobs” to manage operational
risk in portfolio‟s of monitored assets
• It‟s an “early warning system” .. For emerging/ systemic issues
• Effective risk transfer mechanism .. From unplanned to planned maintenance
(c) General Electric Company - 2010 19

Summary .. “Actuarial Engineering”
An “engineering only” approach cannot unlock PHM‟s full value .. the
associated financial service & business process is just as important
“Actuarial Engineers” .. Engineers with skills in Operations Research,
PHM, Reliability & Actuarial Science … are the people who can run the
business of PHM
This field requires collaboration between the engineering and actuarial
communities .. need to learn the other person‟s language ..
Exciting area for research !!
Thank You !
(c) General Electric Company - 2010
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