RELIABILITY BASED ANALYSIS OF A FLEET                                                 OF        TRANSPORTATION VEHICLES   ...
Problem Statement       Objective : Exploring the design of a health management strategy for a        fleet of vehicles t...
SoS ROPE -diagramLevel        Resources                    Operations                   Economics                      Pol...
SoS FeaturesDiscriminating Factor                                 ApplicabilityManagerial independence      Component syst...
Abstraction    Various Actors in the System                                            Command       Command Center: Cent...
Problem formulation    Task 1 : Construct a reliability based model of an                          APC    Task 2 : Constru...
An Agent Based SoS ModelType of Model used : Agent based model for representing a fleet ofvehiclesWhy ABM ?•Possibilities ...
System Block Diagram                                                 Navigation                                           ...
Primer on Reliability calculations       Instantaneous Failure Rate:       Hazard rate:n = Characteristic life of the co...
Primer on Reliability calculations    Instantaneous Availability    Operational Availability    10                      ...
Agent Based SoS Model - DescriptionObjects (agents)        Vehicles, Fleet commander, service center, and command centerPa...
Command Center                                   Mission feedback                                                         ...
Data List         Vehicle ID                                                  Global Time                                 ...
Important Assumptions   Reliability Model follows a Weibull Distribution   Prognostic Equipment does not fail   Fleet s...
Vehicle States DefinitionS0:   vehicle in standby                   a: failure probabilities for a block of a vehicleS1:  ...
Paper ModelVehicleInput :                    Functions :               Output:Nvehicles, Uptimer         Vehicle_Status( )...
Paper ModelService CenterInput:               Functions:                 Output:                     Delay_repair( )torepa...
Control VariablesFixed Factors                     Random FactorsNumber of Vehicles                Probability of Failure ...
Model Implementation & Verification    Difficult to attain “real world” input parameters, order of     magnitude of input...
Results and Outcomes                              Could not run a full factorial design within project time              ...
Operational Availability Gradient# OF STANDBY VEHICLES                            PROGNOSTIC REPAIR THRESHOLD             ...
Operational Availability Gradient     PROBABILITY OF ACC. USE          IN MISSION                               SERVICE CA...
# of vehicles                                                      Threat Level                                          ...
Validation for Prognostic Repair                 Prognostic Repair              Total Cost              Operational Cost  ...
Validation for Prognostic Repair             Prognostic Repair              Total Cost              Operational Cost      ...
Validation for Prognostic Repair                 Prognostic Repair              Total Cost              Operational Cost  ...
Mission Status Consideration                                 Fraction of Mission Success Gradient                         ...
Fraction of Service Center Occupancy GradientPROGNOSTIC REPAIR THRESHOLD                                                  ...
Total Cost (over 5 years) GradientMINIMUM # OF STANDBY VEHICLES                                    PROGNOSTIC REPAIR THRES...
Total Cost Gradient                    3                                                                                  ...
Operational Cost (over 5 years) GradientMINIMUM # OF STANDBY VEHICLES                                           PROGNOSTIC...
Uncertainty Considerations                                                           Level                                ...
Sensitivity Analysis               Residuals              Mean Oper Availability                                          ...
Take Aways    Threshold for prognostic repair has a significant effect on:        The more prognostic repairs, the highe...
References    References    Knéé, H. E., Gorsich, D. J., Kozera, M. J., Oak Ridge National Laboratory , “ITS Technologie...
Questions/Comments/Suggestions?                                              Special Thanks To:                           ...
Upcoming SlideShare
Loading in …5
×

Reliability Analysis of a Fleet of Transportation Vehicles

1,532 views

Published on

Published in: Education, Business, Technology
0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total views
1,532
On SlideShare
0
From Embeds
0
Number of Embeds
5
Actions
Shares
0
Downloads
0
Comments
0
Likes
3
Embeds 0
No embeds

No notes for slide

Reliability Analysis of a Fleet of Transportation Vehicles

  1. 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. 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. 3. SoS ROPE -diagramLevel 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 3 Final Project, Team R.A.F.T
  4. 4. SoS FeaturesDiscriminating Factor ApplicabilityManagerial 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. 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. 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 operation6 Final Project, Team R.A.F.T
  7. 7. An Agent Based SoS ModelType of Model used : Agent based model for representing a fleet ofvehiclesWhy 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 bethought 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 multiplepossibilities of interaction•Naturally group able homogeneous entities i.e fleet of vehicles, service station etc. 7 Final Project, Team R.A.F.T
  8. 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 BlockEngine 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 RadioEngine sensory array system Hydraulic Ignition Braking system Display system system system Lighting system 8 Final Project, Team R.A.F.T
  9. 9. Primer on Reliability calculations Instantaneous Failure Rate: Hazard rate:n = Characteristic life of the component (scale parameter)β = shape parameter of Weibull distributiont = time ( we assume time step = 1)Since we have a series configuration with no redundancy. Thehazard rate of the block will be the sum of hazard rates ofindividual components of that block 9 Final Project, Team R.A.F.T
  10. 10. Primer on Reliability calculations Instantaneous Availability Operational Availability 10 Final Project, Team R.A.F.T
  11. 11. Agent Based SoS Model - DescriptionObjects (agents) Vehicles, Fleet commander, service center, and command centerParameters - Capabilities of vehicles - Reliability of vehicle capabilities - Number of ready vehicles - Cost , Mission IDStates - For SC, full capacity - Vehicles- in mission, failed , in service, serviced , stand by - Mission – complete , in schedule, failedSpace - NetworkTime - Discrete Time Steps (step size = 1 day), over 5 yearsAdjustable 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. 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 CenterReliability data Repair Source Track Vehicle Parts Cost Final Project, Team R.A.F.T 12
  13. 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. 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. 15. Vehicle States DefinitionS0: vehicle in standby a: failure probabilities for a block of a vehicleS1: vehicle on mission b: open slots in service centerS2: vehicle has failed c: prognostic repair thresholdS3: vehicle being repaired d: mission requirements e: number of standby vehiclesSTATE TRANSITIONSF(S0, {a, d}) = S1  vehicle meets requirements and is sent on missionF(S1, a) = S2  vehicle has failed due to degradation 0.5 0F(S2, {a, b}) = S3  vehicle sent for repair 1F(S3, a) = S0  vehicle repair has been completed 1.5 2F(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 15 Final Project, Team R.A.F.T
  16. 16. Paper ModelVehicleInput : Functions : Output:Nvehicles, Uptimer Vehicle_Status( ) • Reliability of subsystem at T in a blockstatus Par_block( ) [8 blocks] • Total Block Reliability Replaced ( ) • Updated substate & state in a Damaged ( ) subsystem Substate ( ) • Failed vehicles Serviced ( ) • Uptimer status Fuel_Eff( )Fleet CommanderInput : 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 orReliability 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. 17. Paper ModelService CenterInput: Functions: Output: Delay_repair( )torepair _comm Cost _ repair ( ) • Cost and Delay –for repair and replacetoreplace_comm Delay_replace ( ) [N X 8 , array ]tojunk-comm Cost_replace ( ) • Vehicle status (in use, in service, servicedapproved_service Vehicle _status( ) , repairing parts, parts replaced ) Curr_Capc ( ) • Current capacity of SCMissionInput: Function: Output : Damage_block ( )[8 • Current State of Mission [ ongoing ,mission_idtime blocks] complete, failed]mission-Id Vehicle _status( ) • Damage of the Blockmission _req Vehicle_mission( ) • Updated Vehicle missionthreat_level Mission_match( ) • Mission Id of each vehicle. Mission_status( ) Global_time( ) 17 Final Project, Team R.A.F.T
  18. 18. Control VariablesFixed Factors Random FactorsNumber of Vehicles Probability of Failure (reliability)Characteristic life Mission RequirementsShape parameter Mission Threat LevelService Center Size Probability of Accelerated DamageThreshold for Prognostic Repair Restoration through RepairMin.Vehicles on StandbyUseful life of VehicleDelay/Cost of RepairsDelay/Cost of ReplacementDelay/Cost of New VehicleCost-Delay Tradeoff WeightsWeights for Operational Cost
  19. 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. 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
  21. 21. Operational Availability Gradient# OF STANDBY VEHICLES PROGNOSTIC REPAIR THRESHOLD Final Project, Team R.A.F.T 23
  22. 22. Operational Availability Gradient PROBABILITY OF ACC. USE IN MISSION SERVICE CAPACITY (# OF VEHICLES ALLOWED)24 Final Project, Team R.A.F.T
  23. 23. # of vehicles  Threat Level 20 Low 20 Medium 20 High Time  18 18 18 16 16 16 14 14 14 12 12 12 1 10 8 10 8 10 8 Functional 6 4 6 4 6 4 Vehicles 2 2 2 0 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 20 20 20 Standby 18 18 18 16 16 16 Vehicles 14 14 14 12 12 12 Available 5 10 8 10 8 10 8 6 6 6 Service 4 4 4 Slots 2 2 2 0 0 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 20 20 20 Service Capacity 18 18 18 16 16 16 14 14 14 12 12 12 10 10 8 10 8 10 8 6 6 6 4 4 4 2 2 2 0 0 200 400 600 800 1000 1200 1400 1600 Final Project, Team R.A.F.T 1800 2000 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0 200 400 600 800 1000 1200 1400 1600 25 1800 2000
  24. 24. Validation for Prognostic Repair Prognostic Repair Total Cost Operational Cost 16 Prognostic Repair Threshold = 0.25 14 12 10COST 8 6 4 2 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Final Project, Team (DAYS) TIME R.A.F.T 26
  25. 25. Validation for Prognostic Repair Prognostic Repair Total Cost Operational Cost 14 Prognostic Repair Threshold = 0.50 12 10 8COST 6 4 2 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Final Project, Team (DAYS) TIME R.A.F.T 27
  26. 26. Validation for Prognostic Repair Prognostic Repair Total Cost Operational Cost 12 Prognostic Repair Threshold = 0.75 10 8COST 6 4 2 0 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Final Project, Team (DAYS) TIME R.A.F.T 28
  27. 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 Final Project, Team R.A.F.T
  28. 28. Fraction of Service Center Occupancy GradientPROGNOSTIC REPAIR THRESHOLD Service Center Capacity Final Project, Team R.A.F.T 30
  29. 29. Total Cost (over 5 years) GradientMINIMUM # OF STANDBY VEHICLES PROGNOSTIC REPAIR THRESHOLD Final Project, Team R.A.F.T 31
  30. 30. Total Cost Gradient 3 untitled fit 1 z vs. x, y 2.8 2.6 2.4THREAT 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 Final Project, Team R.A.F.T 32
  31. 31. Operational Cost (over 5 years) GradientMINIMUM # OF STANDBY VEHICLES PROGNOSTIC REPAIR THRESHOLD Final Project, Team R.A.F.T 33
  32. 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 data34 Final Project, Team R.A.F.T
  33. 33. Sensitivity Analysis Residuals Mean Oper Availability Residuals # Functional 1 200.8 150.6 100.4 50.2 0 0 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 -5-0.2 Residuals Total Cost 1.20E+06 1.00E+06 8.00E+05 6.00E+05 4.00E+05 2.00E+05 0.00E+00 1 2 3 4 5 6 7 8 9 10 -2.00E+05 -4.00E+05 Final Project, Team R.A.F.T 35
  34. 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. 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
  36. 36. Questions/Comments/Suggestions? Special Thanks To: Mark Smith Hai Le Matthew Hoffman38 Final Project, Team R.A.F.T

×