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PGM risk Sensitivity Analysis
20 July 2008Henry Neimeier
OWS Threads
U S A R M Y
Air LayerRadioSATCOM Fiber GPS/GBS
National Assets Reachback
Fiber Node
Fiber Node
Ground Station
Theatre C2 Node
Tactical C2 Node Ground
Station
CSG C2 Node
PGM risk Player Interface: green/gray buttons inputs, red buttons output results
Portfolio
MOEs
Scenario Options PGM risk
Air Layer
Scenario Parameters
Stepwise Regression
Rank Correlation
Tornado Uncertain All Inputs
Elastic ity MOE % change
from 1% change In Input
Sensitivity Analysis
ModelDetails
(proportion) :Corrected Pk Calc
(minutes) :Path … Calc
Survivable Throughput Calc
(probability) :Path Survival Calc
(proportion) :Link Thruput Calc
Targets At Risk Calc
Select Alt… Edit Table
(seconds/link) :Service Time Edit Table
Link Survival Probability Edit Table
Priority Proportion Edit Table
Utilization Edit Table
Baulking Utilization 0.8
Nodes 300
Setup Proportion 0.05
Pclassify Calc
(minutes) :Revisit Calc
(km2) :AOIsc Edit Table
ISR Platform Select Edit Table
ISR Parameters Edit Table
(m) :Target Size Edit Table
(probability) :Escape Calc
(hz) :Theater Aerial … Calc
Relay Planes Calc
(minutes) :Enemy Respon… Edit Table
(km) :Move Distance Edit Table
(km/hr) :Speed Edit Table
(minutes) :Pause Edit Table
Proportion Update 0.5
Kills Per Sortie Edit Table
Loadout Edit Table
(Hz) :Bandwidth Edit Table
(knots) :Speed Edit Table
(hours) :Endure Edit Table
(ft) :Relay Altitude Edit Table
(nmi) :Base Range Edit Table
(dollars) :Cost Edit Table
Payload Lb Hrs/AC $ Calc
Average Pk Calc
Select Scenario MCO2
Select Threat Level Low Intensity
Select Path Cell overfly
(Regression Coe) :Pk … Result
(Regression Coe) :Avg Pk Reg Calc
(Regression Coe) :Path Survival Reg Calc
(Regression Coe) :Survivable Thruput Reg Calc
(Regression Coe) :Path Delay Reg Calc
(Rank Correlation) :Pk RC Calc
(Rank Correlation) :Avg Pk RC Calc
(Rank Correlation) :Path Survival RC Calc
(Rank Correlation) :Survivable Thruput RC Calc
(Rank Correlation) :Path Delay RC Calc
(kill probability) :Pk T Calc
(kill probability) :Avg Pk T Calc
(probability) :Path Survival T Calc
(proportion) :Survivable Thruput T Calc
(minutes) :Path Delay T Calc
(kill probability) :Pk T Calc
(probability) :Path Survival T Calc
(kill Probability) :Avg Pk T Calc
(proportion) :Survivable Thruput T Calc
(minutes) :Path Delay T Calc
(%) :Pk Elasticity Calc
(%) :Average Pk Elasticity Calc
(%) :Path Survival Elasticity Calc
(%) :Survivable Thruput Elasticity Calc
(%) :Path Delay Elasticity Calc
Select Alternatives Edit Table
(minutes) :Outage Time Edit Table
Model Details (Module InfluenceDiagram & Module
Summary)
Portfolio: Selects scenario options, calculates TLE, and sets uncertain input variable distributions.Target Movement: Calculates target escape probability from target movement statisticsWeapons: Assigns weapons to target classes to maximize effective kills persortie corrected for target location error TLE, survivable throughput, escape probabilityComm Net: Calculate path delay, path survival probability, and survivable throughputfor specified network parameters and threat levelKill Thread Delay: Set thread task, sense, fuse, plan, execute times.Compare total time to enemy response time to determine targets at risk.ISR: Assigns ISR platforms to scenario, calculates revisit time, & probability of target classificationTerrain Weather: Calculates ISR coverage multiplier to correct for scenario weather and terrain masking.
indiciesfunctions
TargetMovement
ISR
Weapons
Kill ThreadDelay
Air Layer
Comm Net
Portfolio
TerrainWeather
SensitivityAnalysis
Overview
Portfolio Module: Specifies uncertain input variable distribution and selects scenario options
10.8 0.90.75 0.85 0.950
1
0.10.20.30.40.50.60.70.80.9
LinkSur
Cu
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lati
ve
Pro
ba
bil
ity
Link UpgradeNo Yes
Input Chance VariableTriangular DistributionsLight Blue Ellipses
TLE*Drift Rate
Service Time
Node Degree
Traffic ExtentPower
Link SurvivalProbability
SelectAlternatives
CA
CS
Link Survival
COSTTotal
AlternativeCost
Node DegUncertainty
Term Acc
Link Surv
Traf Pwr
SelectScenario
Select ThreatLevel
Service Tm
CV Ar
CV Svtm
svtms
TerminalAccess
Select LinkUpgrade
Outage Time Outage Out Tm
TLE
TLE multiplier of kill probability
Kill Thread Delay
Processing
STS DelayExecute
ExecuteUncertainty
Revisit
EnemyResponse Tm
Remaining TimeDistribution
Total Task TimeDistribution
Sense
Plan &Deconflict
Task Time
Task TimeDistribution
Total TaskTime
RemainingTime
Task ISR
Fuse &Integrate
Targets AtRisk
Path Delay
ExecutePriority
Comm Delay
RedResponse Tm
Select ThreatLevel
Execute Time
Weapons
Average Pk
Kills PerSortie
Loadout
Cost
ExpectedKills
MaxExpected
Kills
Pk
PotentialPlatforms
PlatformSpeed
Execute Time standoff
Range BandDistsnce
speed
CAP
WeaponAssigned Kills/Sortie
type
FastestStrike
Platform
CAP Direct
GPS
TLE*Probability
UpdateEscape
SurvivableThroughput
TactomProportion
ExpectedKills TacticalTommahawk
Pk Avg
Range BandProportion
Target ClassProportion
total
total
Targets AtRisk
Classification
Pk Cor
Kill probability is product of following factors:TLE multiplier (Portfolio)Effective kill probability per sortie (Weapons)Probability of classification (Weapons)Proportion of time SA fixed (TacTom)Probability of escape (Target motion)Survivable throughput (Comm)Targets at risk (Kill Thread)
Expected Kills Per Sortie Weapons Input (nominal Unclassified)
Sensitivity Analysis• Model non linear in both functions and interactions (products) of factors
– Sensitivity results vary by input variables not selected– Operating point effects sensitivity– Global versus local techniques
• Analytica supports both deterministic (analytic) and simulation modes in same model (output display option)
– Deterministic (mid) mode-fast same answer each time (analytic)– Chance probability distribution – slower slightly different answer with different
random number seeds (simulation)• Selected techniques: Tornado Diagrams, Elasticity, Rank Correlation,
Stepwise Regression, Orthogonal Factorial Designs, Correlation & Partial correlation
• Note the PGM risk model was developed in Analytica that supports the above sensitivity analysis techniques directly
Reference: Sensitivity Analysis by A. Saltelli…
Y
X
Sensitivity Analysis ModulesSensitivity Analysis Tornado
Regression
Elasticity
Rank Correlation
Average PkCorrected Pk
Tornadoes ImportanceElasticity
Path Survival Path DelaySurvivableThroughput
StepwiseRegression
SensitivityAnalysisLibrary
RankCorrelation
Vars
Input Ranges
Average Pk
Avg Pk T
Average PkInput Ranges
Level
Pk T
Path Delay TPath SurvivalT
SurvivableThruput T
Corrected Pk
All PlayerInputs
All PlayerInputs
Average PkElasticity
Pk Elasticity
Path SurvivalElasticity
Path DelayElasticity
Chance PkInputs
SurvivableThruputElasticity
Pk Elasticity
Path SurvivalElasticity
SurvivableThruputElasticity
Path DelayElasticity
Average PkElasticity
Corrected PkTop
Pk Details
Average Pk
AvgPkDetails
AvgPkNumber
AvgPk InputDescriptor
Avg Pk Reg
Pk Number
Pk InputDescriptor
Pk Reg
Path SurvivalSurvivableThroughput
Surv ThruDetails
Surv ThruNumber
Surv ThruDescriptor
SurvivableThruput Reg
Path Delay
Delay Details
DedlayNumber
DelayDescriptor
Path DelayReg
SurvivalDetails
Delay Mode
SurvivalNumber
SurvivalDescriptor
Path SurvivalReg
SelectPriority
Corrected PkTop
Pk Details
Average Pk
AvgPkDetails
AvgPkNumber
AvgPk InputDescriptor
Avg Pk RC
Pk Number
Pk InputDescriptor
Pk RC
Path SurvivalSurvivableThroughput
Surv ThruDetails
Surv ThruNumber
Surv ThruDescriptor
SurvivableThruput RC
Path Delay
Delay Details
DedlayNumber
DelayDescriptor
Path DelayRC
SurvivalDetails
Delay Mode
SurvivalNumber
SurvivalDescriptor
Path SurvivalRC
SelectPriority
Tornado Diagrams• Select output variable (MOE)• Select Input variables and low, baseline, and high values for them• Calculate output variable values for low and high values of the
selected input variable with all other input values at their baseline values
• Repeat for each successive input variable• Sort the input variables in decreasing order of the high-low output
MOE values– Note changes in non selected input values can change order (non
monotonic tornado values)• Many real world processes are not controllable
– Weather, enemy actions, time delays..– Tornado process assumes total parameter control of all input variables
• Handles both fixed and chance variable distributions – Distribution parameter values (min, mode, max…) controllable
Example Tornado Results(MOE: kill probability, average kill probability, priority 1 path delay)
MCO2, All Options, Low Intensity, Cell Overfly, Link Upgrade
Explanation Of Example Tornado Plot
• Input variables in order of significance to medium ship kill probability included link survival probability, red response time, network utilization, baulking utilization
• Input variables were changed by +10% (high) and -10% (low) from the baseline case• Operating point:
– Threat level: low intensity– All options selected– The target class is medium ship– The target is in the 40-150 kilometer range band
• Baseline kill probability for the operating point is 37%• Raising the link survival probability by 10% improves the kill probability to 51%• Lowering the link survival probability by 10% reduces the kill probability to 23%• Increasing red response time by 10% increases kill probability to 41• Decreasing red response time by 10% reduces the kill probability to 33%• Increasing utilization by 10% reduces kill probability to 33%• Decreasing utilization by 10% increases kill probability to 41%• Other parameters have less impact• Non linear system: high and low bars different lengths• Other MOEs shown are: average kill probability, communication path delay in minutes, and
survivable throughput.