Fostering Friendships - Enhancing Social Bonds in the Classroom
Reliability Analysis of a Fleet of Transportation Vehicles
1. RELIABILITY BASED ANALYSIS OF A FLEET OF
TRANSPORTATION VEHICLES
Army vehicle fleet. Photo released by US Army
Team ‘R.A.F.T.’
Bill Bernstein
Devarajan Ramanujan
Akanksha Sinha
AAE 560, Purdue University, Spring 2012
In conjunction with the Health Management Project laid out by Sandia National Labs.
2. Problem Statement
Objective : Exploring the design of a health management strategy for a
fleet of vehicles through a reliability based model.
An Armored Personnel Carrier (APC) is taken as a case study. Note:
A HMMWV M1114 was used for estimates.
Constraints :
Efficient operation : A cap on the minimum efficiency of operation.
Logistical constraints – repair cost and availability of repair stations.
Preference : Decision makers decides the preference
Cost, Repair stations size and efficient operations
Need :
Modeling system reliability based on optimizing operational costs
while managing the operational availability of a fleet .
2 Final Project, Team R.A.F.T
3. SoS ROPE -diagram
Level Resources Operations Economics Policy
α Vehicles, personnel Operating a resource Economics of Policies relating to
and infrastructure (e.g. the vehicle itself) operating/buying/ leasing a single-resource use
(e.g. cargo trucks, resource - Vehicle (e.g. vehicle
roads) operating costs (VOC), operating
maintenance costs procedures)
β Collection of Operating resource Economics of Policies related to
resources for a networks for common operating/buying/ leasing a vehicle fleet (e.g.
common function function (e.g. fleet fleet, resource network emissions, fuel
(e.g. vehicle fleet) management) (e.g. maintenance centers) efficiency)
γ Collection of Operations of Economics of mission Policies regulating
resources for a collections resource deployment – e.g. man various sectors
mission – multiple networks – e.g. hours, degradation of using multiple
types of vehicle fleets mission deployment mission inventory vehicles, draft
(e.g. cargo, heavy committees
tank)
δ Army transportation Operations of entire Cost of military Military
system Army Transportation transportation needs transportation
System policies
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4. SoS Features
Discriminating Factor Applicability
Managerial independence Component systems are acquired by separate program
offices and run by separate operation units.
Operational independence Connected by a military command and control network, which is
integrating in both the technical and social sense. Each
component is granted limited operational independence to
respond to unforeseen and uncontrolled events.
Stable intermediate forms Stable intermediate forms are achieved in our model by having a
threshold of vehicles in “stand by” and not sending all the
vehicle at one time to SC or mission or both.
Policy triage Single service systems are centrally directed, but the command
centre does not fully control either the development or the
modes of operation of these system.
Ensuring collaboration Largely achieved through socio technical methods of
command and control .
Leverage at the interfaces System trade cost ,delays and performances among components.
Directed SoS
4 Central command, has theTeam R.A.F.T authority
Final Project, controlling
5. Abstraction
Various Actors in the System Command
Command Center: Central authority that center
makes all top-level decisions
Fleet
Fleet Commander: Responsible for the commander
efficient working of entire fleet of
Vehicle , Service center ,
vehicles Warehouse, Missions
Vehicle: A generic Armored Personal
Carrier’ (APC) equipped with required Mission
mission capabilities
Service center: A repair station for Fleet Command Warehouse
Commander center
malfunctioning APC’s
Ware House: It stocks various parts and
new fully-built APCs Vehicle Service
center
Mission: A task that the vehicle fleet, has
to perform
5 Final Project, Team R.A.F.T
6. Problem formulation
Task 1 : Construct a reliability based model of an
APC
Task 2 : Construct an agent based SOS model for
representing a fleet of vehicles
Task 3: Modeling the maintenance scheme
Task 4: Establishing business rules of operation
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7. An Agent Based SoS Model
Type of Model used : Agent based model for representing a fleet of
vehicles
Why ABM ?
•Possibilities of Emergent behavior from the model
•Combination of social and technical systems
•Primary goal is to study states of vehicles (operational / under repair). They can be
thought of as ‘objects’
•Very little historical data. Several parameters cannon cannot be exactly quantified
•Interested in modeling complexity due to hierarchy in decision model and multiple
possibilities of interaction
•Naturally group able homogeneous entities i.e fleet of vehicles, service station etc.
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8. System Block Diagram
Navigation
Block
Engine Block
Structural Block
Firing Block
Engine Sat-com Structural Target
assembly system Assembly Acquisition
system
Engine Navigation Suspension
Lubrication system system Secondary firing
system system
Body
Drivetrain Block
Engine Cooling Armor
system Primary firing
Steering system
system
Fuel supply
Misc. Block
system Fire control
Transmission Air conditioning system
system system
Exhaust
system Wiper Electronic
Wheel Assembly system Countermeasure
Firing
system
Auxiliary Block
Communication
Block
Tire Electrical Supply
Pneumatics system Radio
Engine sensory
array system
Hydraulic
Ignition Braking system
Display
system system
system
Lighting
system
8 Final Project, Team R.A.F.T
9. Primer on Reliability calculations
Instantaneous Failure Rate:
Hazard rate:
n = Characteristic life of the component (scale parameter)
β = shape parameter of Weibull distribution
t = time ( we assume time step = 1)
Since we have a series configuration with no redundancy. The
hazard rate of the block will be the sum of hazard rates of
individual components of that block
9 Final Project, Team R.A.F.T
10. Primer on Reliability calculations
Instantaneous Availability
Operational Availability
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11. Agent Based SoS Model - Description
Objects (agents) Vehicles, Fleet commander, service center, and command center
Parameters - Capabilities of vehicles
- Reliability of vehicle capabilities
- Number of ready vehicles
- Cost , Mission ID
States - For SC, full capacity
- Vehicles- in mission, failed , in service, serviced , stand by
- Mission – complete , in schedule, failed
Space - Network
Time - Discrete Time Steps (step size = 1 day), over 5 years
Adjustable Variables Reliability (Weibull parameters ) , Capacity of SC ,Number of
vehicle ( fleet size), Delay time ,Missions frequency , Cost , Service
thresholds (prognostics)
Stochastic Parameters Delays ,Random failures ,Time to failure (TBF) ,Time to repair
(TTR), Likelihood of threats, mission requirements,
11 Final Project, Team R.A.F.T
12. Command Center
Mission feedback
Mission Cost
Vehicles Generator Reviewing
Track Reliability
Mission definition
Fleet Commander
Reliability data
Operations log
Repair Mission
Decisions Decisions
Job details
Service Center
Reliability data
Repair Source Track
Vehicle Parts Cost
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13. Data List
Vehicle ID Global Time
Vehicles
Reliability data Vehicle States
Uptime & Life tracker
Vehicle list Mission ID
Service Center
Delay logger Mission Spacing
Capacity logger #Vehicles
Cost estimator Instantaneous survival
probability:
Commander
Repair decision logic Engine Block >0.95
Fleet
Drive train Block >0.95
Mission decision logic Structural Block >0.85
Final Project, Team R.A.F.T 13
14. Important Assumptions
Reliability Model follows a Weibull Distribution
Prognostic Equipment does not fail
Fleet size remains constant
Mission requirements are random
No shortage of spares at the service center
Service center has a fixed workday length
Randomization in vehicle selection for a mission
Randomization in order of prognostic repair
15. Vehicle States Definition
S0: vehicle in standby a: failure probabilities for a block of a vehicle
S1: vehicle on mission b: open slots in service center
S2: vehicle has failed c: prognostic repair threshold
S3: vehicle being repaired d: mission requirements
e: number of standby vehicles
STATE TRANSITIONS
F(S0, {a, d}) = S1 vehicle meets requirements and is sent on mission
F(S1, a) = S2 vehicle has failed due to degradation 0.5
0
F(S2, {a, b}) = S3 vehicle sent for repair 1
F(S3, a) = S0 vehicle repair has been completed 1.5
2
F(S0, {a, b, c, e}) = S3 vehicle sent for prognostic repair 2.5
3
3.5
4
4.5
5
0 1 2 3 4 5 6
nz = 11
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16. Paper Model
Vehicle
Input : Functions : Output:
Nvehicles, Uptimer Vehicle_Status( ) • Reliability of subsystem at T in a block
status Par_block( ) [8 blocks] • Total Block Reliability
Replaced ( ) • Updated substate & state in a
Damaged ( ) subsystem
Substate ( ) • Failed vehicles
Serviced ( ) • Uptimer status
Fuel_Eff( )
Fleet Commander
Input : Functions : Output:
•Approve Vehicles for services (Matrix 1&
Vehicle Status (in use , torepair_comm ( ), 0) ,
failed , in service) , toreplace_comm ( ), •Make decision ( to repair ,to replace or
Reliability block , tojunk_comm ( ) to junk) based on cost and delay matrix ,
Current Capacity SC approved_service ( ) •Number of vehicles -not in service or
on Mission
16 Final Project, Team R.A.F.T
17. Paper Model
Service Center
Input: Functions: Output:
Delay_repair( )
torepair _comm Cost _ repair ( ) • Cost and Delay –for repair and replace
toreplace_comm Delay_replace ( ) [N X 8 , array ]
tojunk-comm Cost_replace ( ) • Vehicle status (in use, in service, serviced
approved_service Vehicle _status( ) , repairing parts, parts replaced )
Curr_Capc ( ) • Current capacity of SC
Mission
Input: Function: Output :
Damage_block ( )[8 • Current State of Mission [ ongoing ,
mission_idtime blocks] complete, failed]
mission-Id Vehicle _status( ) • Damage of the Block
mission _req Vehicle_mission( ) • Updated Vehicle mission
threat_level Mission_match( ) • Mission Id of each vehicle.
Mission_status( )
Global_time( )
17 Final Project, Team R.A.F.T
18. Control Variables
Fixed Factors Random Factors
Number of Vehicles Probability of Failure (reliability)
Characteristic life Mission Requirements
Shape parameter Mission Threat Level
Service Center Size Probability of Accelerated Damage
Threshold for Prognostic Repair Restoration through Repair
Min.Vehicles on Standby
Useful life of Vehicle
Delay/Cost of Repairs
Delay/Cost of Replacement
Delay/Cost of New Vehicle
Cost-Delay Tradeoff Weights
Weights for Operational Cost
19. Model Implementation & Verification
Difficult to attain “real world” input parameters, order of
magnitude of inputs were estimated based on intuition
and available literature (e.g. labor costs, fleet size, etc.)
Code was development in a modular fashion in order to
test “along the way”.
Each module was thoroughly tested early and results
were qualitatively assessed on the basis of general
feasibility.
One particular problem was our fuel efficiency
degradation estimate…
19 Final Project, Team R.A.F.T
20. Results and Outcomes
Could not run a full factorial design within project time
constraints (too many control variables)
Selected most important control variables to vary after
teleconference meeting with Sandia (examples below)
Mostly tested w.r.t. Total Cost and Operational Availability
# OF STANDBY VEHICLES
SERVICE CENTER CAP.
THREAT LEVEL
THREAT LEVEL
PROGNOSTIC REPAIR THRESHOLD SERVICE CAPACITY # OF STANDBY # OF STANDBY
22 Final Project, Team R.A.F.T
24. Validation for Prognostic Repair
Prognostic Repair Total Cost Operational Cost
16
Prognostic Repair Threshold = 0.25
14
12
10
COST
8
6
4
2
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
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TIME R.A.F.T 26
25. Validation for Prognostic Repair
Prognostic Repair Total Cost Operational Cost
14
Prognostic Repair Threshold = 0.50
12
10
8
COST
6
4
2
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
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TIME R.A.F.T 27
26. Validation for Prognostic Repair
Prognostic Repair Total Cost Operational Cost
12
Prognostic Repair Threshold = 0.75
10
8
COST
6
4
2
0
0 200 400 600 800 1000 1200 1400 1600 1800 2000
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TIME R.A.F.T 28
27. Mission Status Consideration
Fraction of Mission Success Gradient Fraction of Missions Met Gradient
15 15
# OF STANDBY VEHICLES
untitled fit 1 untitled fit 1
z vs. x, y z vs. x, y
14 14
13 13
12 12
11 11
10 10
y
y
9 9
8 8
7 7
6 6
5 5
0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75
x x
Prognostic Repair Threshold Prognostic Repair Threshold
29
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28. Fraction of Service Center Occupancy Gradient
PROGNOSTIC REPAIR THRESHOLD
Service Center Capacity
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29. Total Cost (over 5 years) Gradient
MINIMUM # OF STANDBY VEHICLES
PROGNOSTIC REPAIR THRESHOLD
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30. Total Cost Gradient
3
untitled fit 1
z vs. x, y
2.8
2.6
2.4
THREAT LEVEL
2.2
2
y
1.8
1.6
1.4
1.2
1
1 2 3 4 5 6 7 8 9 10
x
# OF SERVICE SLOTS
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31. Operational Cost (over 5 years) Gradient
MINIMUM # OF STANDBY VEHICLES
PROGNOSTIC REPAIR THRESHOLD
Final Project, Team R.A.F.T 33
32. Uncertainty Considerations
Level Nature
Location Statistical Scenario Recognized Epistemic Variability
uncertainty uncertainty uncertainty uncertainty uncertainty
Natural, Definition of fleet,
Independence and Level of
Technological, mission.
correlation in abstraction of System to system
Context Economic, Social
system technological
Stakeholders.
variability
and Political Command
representation system
representation structure
Fidelity of Topology of RBD
Parameters of Future state of BKI reliability model system, True Random failures,
Model structure
Reliability model model of agents with real data utility structure of random delays
Model DM
Characterization
Sampling method Sequential / True distribution
Technical model of true
for parameters Parallel operations of noise
distribution
Future state of Bias,
True decision Preference
Driving forces MTBF, MTTR vehicle, Nature of Communication
model of DM weights of MCDA
Inputs mission delays
Data on APC Time period of Failure Failure modes,
System data
reliability operations. mechanisms Timescales
Availability,
Hazard rate, Operational BKI models of Mission specs, BKI Delays,
Parameters Delays availability, Mission agents models of agents Component Life
Assumptions
Case based Literature review Incorporates
Modeling Strategies Confidence limits
reasoning
based on historical
and historical data probabilistic noise
data
34 Final Project, Team R.A.F.T
34. Take Aways
Threshold for prognostic repair has a significant effect on:
The more prognostic repairs, the higher the operational availability
As of now, total/operational cost is sensitive to input
parameters
Perform a full factor covariance analysis to determine significant
factor effects ( random and fixed)
There exists a tradeoff between percentage occupancy of
service center and total cost.
For no delays a service center size =7 is the best design option
Increasing threat level increases total cost and service center
occupancy. Operational availability is reduced
By performing an experiment with more replicates we will be
able to analyze trends related to:
The effect of number of vehicles in standby
Effect of Weibull parameters on the model results
36 Final Project, Team R.A.F.T
35. References
References
Knéé, H. E., Gorsich, D. J., Kozera, M. J., Oak Ridge National Laboratory , “ITS Technologies in Military
Wheeled Tactical Vehicles: Status Quo and the Future,” ITS-America 2001 Conference (11th Annual Meeting and
Exposition), Miami Beach, FL (US),. 2001.
DeLaurentis, D. A. (2008) Understanding Transportation as a System of Systems Problem, in System of
Systems Engineering (ed M. Jamshidi), John Wiley & Sons, Inc., Hoboken, NJ, USA
Dekker, R., “Applications of maintenance optimization models: a review and analysis”, Reliability Engineering &
System Safety,Vol. 51, No. 3, 1996, pp. 229-240.
Sherif,Y.S., and Smith, M.L. (1981), "Optimal maintenance models for systems subject to failure-A review",
Naval Research Logistics Quarterly 28, 47-74.
C. E. Love and R. Guo Utilizing Weibull Failure Rates in Repair Limit Analysis for Equipment
Replacement/Preventive Maintenance Decisions, Jour. of the Operational Research Society, 47, 1366 - 1376.
B. H. Mahon and R. J. M. Bailey, “A proposed improved replacement policy for army vehicles, J. Opl Res. Soc.,
26, 477-494, 1975.
Vachtsevanos, G., Lewis, F., Roemer, M., Hess, A. and Wu, B. (2007) Frontmatter, in Intelligent Fault Diagnosis
and Prognosis for Engineering Systems, John Wiley & Sons, Inc., Hoboken, NJ, USA
Wilmering, T.J.; Ramesh, A.V. , "Assessing the impact of health management approaches on system total cost
of ownership," Aerospace Conference, 2005 IEEE , vol., no., pp.3910-3920, 5-12 March 2005
R.J. Ellison, D.A. Fischer, R.C. Linger, H.F. Lipson, T. Longstaff, N.R. Mead, “Survivable network
systems: an emerging discipline”, Technical Report CMU/SEI-97-TR-013, November 1997, revised May 1999.
P. O’Connor, Practical Reliability Engineering, 4th ed., John Wiley & Sons, Inc., Hoboken, NJ, USA, 2002.
37 Final Project, Team R.A.F.T
