Prognostics and Logistics. Tim Felke 2009 PHM Conference San Diego, CA

Transcription

1 Prognostics and Logistics Tim Felke 2009 PHM Conference San Diego, CA

2 Agenda Overview of the Logistics Problem Opportunities for PHM to Reduce Logistics Cost Challenges in Realization of Opportunities 2 Honeywell Condition Based Maintenance

3 Logistics: Definition Logistics - (business definition) Logistics is defined as a business planning framework for the management of material, service, information and capital flows. It includes the increasingly complex information, communication and control systems required in today's business environment. -- (Logistix Partners Oy, Helsinki, FI, 1996) Logistics - (military definition) The science of planning and carrying out the movement and maintenance of forces... those aspects of military operations that deal with the design and development, acquisition, storage, movement, distribution, maintenance, evacuation and disposition of material; movement, evacuation, and hospitalization of personnel; acquisition of construction, maintenance, operation and disposition of facilities; and acquisition of furnishing of services. -- (JCS Pub 1-02 excerpt) Logistics - The procurement, maintenance, distribution, and replacement of personnel and materiel. -- (Websters Dictionary) Logistics - The process of planning, implementing, and controlling the efficient, cost effective flow and storage of raw materials, in-process inventory, finished goods and related information from point of origin to point of consumption for the purpose of meeting customer requirements. -- (Reference: Canadian Association of Logistics Management, 12 Feb, 1998) Logistics - The science of planning, organizing and managing activities that provide goods or services. -- (MDC, LogLink / LogisticsWorld, 1997) Logistics - Logistics is the science of planning and implementing the acquisition and use of the resources necessary to sustain the operation of a system. -- (Reference: ECRC University of Scranton / Defense Logistics Agency Included with permission from: HUM - The Government Computer Magazine "Integrated Logistics" December 1993, Walter Cooke, Included with permission from: HUM - The Government Computer Magazine.) What is logistics? "Logistics means having the right thing, at the right place, at the right time." 3 Honeywell Condition Based Maintenance

4 Optimal Inventory Problem Many Logistics Problems Are Similar in Structure to Optimal Inventory Problems in Traditional Operations Management. General Problem: Find the Optimal Inventory Level for an Asset Given an Uncertain Demand and Unequal Costs for Overstock and Understock. Problem Factors: - Demand Statistics (f) Mean (µ) Standard Deviation (σ) - Overstock Cost (C o ) - Understock Cost (C u ) - Quantity Ordered (Q) - Optimal Quantity (Q*) 4 Honeywell Condition Based Maintenance

5 Cost Factors C o = Overstock Cost The cost of ordering one more unit than what you would have ordered had you known demand. In other words, suppose you had left over inventory (i.e., you over ordered). C o is the increase in profit you would have enjoyed had you ordered one fewer unit. C u = Understock Cost The cost of ordering one fewer unit than what you would have ordered had you known demand. In other words, suppose you had lost sales (i.e., you under ordered). C u is the increase in profit you would have enjoyed had you ordered one more unit. 5 Honeywell Condition Based Maintenance

6 Optimal Inventory Problem: Example The Newsvendor Problem is the classic example for the Optimal Inventory Problem. New vendor must place order for papers 1 week in advance. Papers are bought at $0.20 Papers are sold at $1.00 Demand is normal distribution with µ = 10 and σ = 5 Then C o =$1.00-$0.20=$0.80 And C u =$ Honeywell Condition Based Maintenance

7 Optimal Inventory Problem: Try Q=10 These Days You Bought Too Many Q = 10 These Days You Bought Too Few Demand Likelihood Overstock Amount Overstock Cost $1.80 $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00 Expected Co $0.03 $0.04 $0.04 $0.05 $0.05 $0.05 $0.04 $0.03 $0.02 $0.00 Understock Amount Understock Cost $0.80 $1.60 $2.40 $3.20 $4.00 $4.80 $5.60 $6.40 $7.20 $8.00 $8.80 $9.60 $10.40 $11.20 $12.00 $12.80 $13.60 $14.40 Expected Cu $0.06 $0.12 $0.16 $0.19 $0.19 $0.19 $0.17 $0.14 $0.11 $0.09 $0.06 $0.04 $0.03 $0.02 $0.01 $0.01 $0.00 $0.00 Total Overstock Loss = $0.33; Total Understock Loss = $1.58; Total Loss = $ Honeywell Condition Based Maintenance

8 Optimal Inventory Problem: Try Q=12 These Days You Bought Too Many Q = 12 These Days You Bought Too Few Demand Likelihood Overstock Amount Overstock Cost $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00 Expected Co $0.03 $0.04 $0.05 $0.06 $0.07 $0.07 $0.07 $0.06 $0.05 $0.03 $0.02 $0.00 Understock Amount Understock Cost $0.80 $1.60 $2.40 $3.20 $4.00 $4.80 $5.60 $6.40 $7.20 $8.00 $8.80 $9.60 $10.40 $11.20 $12.00 $12.80 Expected Cu $0.05 $0.09 $0.12 $0.12 $0.12 $0.11 $0.09 $0.07 $0.05 $0.04 $0.02 $0.02 $0.01 $0.01 $0.00 $0.00 Total Overstock Loss = $.55 Total Understock Loss = $.92; Total Loss = $ Honeywell Condition Based Maintenance

9 Optimal Inventory Problem: Try Q=14 These Days You Bought Too Many Q = 14 These Days You Bought Too Few Demand Likelihood Overstock Amount Overstock Cost $2.60 $2.40 $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00 Expected Co $0.04 $0.05 $0.07 $0.08 $0.09 $0.09 $0.09 $0.09 $0.08 $0.06 $0.05 $0.03 $0.01 $0.00 Understock Amount Understock Cost $0.80 $1.60 $2.40 $3.20 $4.00 $4.80 $5.60 $6.40 $7.20 $8.00 $8.80 $9.60 $10.40 $11.20 Expected Cu $0.04 $0.06 $0.07 $0.07 $0.06 $0.05 $0.04 $0.03 $0.02 $0.01 $0.01 $0.00 $0.00 $0.00 Total Overstock Loss = $.83 Total Understock Loss = $.48; Total Loss = $ Honeywell Condition Based Maintenance

10 Optimal Inventory Problem: Try Q=16 These Days You Bought Too Many Q = 16 These Days You Bought Too Few Demand Likelihood Overstock Amount Overstock Cost $3.00 $2.80 $2.60 $2.40 $2.20 $2.00 $1.80 $1.60 $1.40 $1.20 $1.00 $0.80 $0.60 $0.40 $0.20 $0.00 Expected Co $0.05 $0.06 $0.08 $0.09 $0.11 $0.12 $0.12 $0.12 $0.11 $0.10 $0.08 $0.06 $0.04 $0.02 $0.01 $0.00 Understock Amount Understock Cost $0.80 $1.60 $2.40 $3.20 $4.00 $4.80 $5.60 $6.40 $7.20 $8.00 $8.80 $9.60 Expected Cu $0.02 $0.04 $0.04 $0.03 $0.03 $0.02 $0.02 $0.01 $0.01 $0.00 $0.00 $0.00 Total Overstock Loss = $1.16 Total Understock Loss = $.22; Total Loss = $ Honeywell Condition Based Maintenance

11 11 Honeywell Condition Based Maintenance Optimal Inventory: Statistical Model C(Q) = overstocking cost(q) + understocking cost(q) + = Q u Q o dx x f Q x C dx x f x Q C Q C ) ( ) ( ) ( ) ( ) ( 0 0 )) ( (1 ) ( ) ( = = Q F C Q F C dq Q dc u o At Q*, Marginal cost of overage at Q* - Marginal cost of underage at Q* = 0 u o u C C C Q D P Q F + = = ) ( ) ( * * Note that this relationship fits to any distribution of f(x). The ratio Cu / (Co + Cu) is called the critical ratio.

12 Interpretation Ordering one more unit increases the chance of overage - Expected loss on the Q th unit = C o x F(Q), where F(Q) = Prob{Demand <= Q) The benefit of ordering one more unit is the reduction in the chance of underage: - Expected benefit on the Q th unit = C u x (1-F(Q)) As more units are ordered, - the expected benefit from ordering one unit decreases - while the expected loss of ordering one more unit increases. 12 Honeywell Condition Based Maintenance

13 Q* with Normal Distribution of Demand If papers are bought at $0.20 and sold at $1.00 Then C o =$1.00-$0.20=$0.80 C u =$0.20 F(Q*) = $0.80 / ($ $0.20) =.8 13 Honeywell Condition Based Maintenance

14 Solving for Optimal Quantity (Q*) F(Q*) = $0.80 / ($ $0.20) =.8 Q* = Honeywell Condition Based Maintenance

15 Change to CDF With Change in σ 15 Honeywell Condition Based Maintenance

16 Effect of Changes of σ on Q* 16 Honeywell Condition Based Maintenance

17 Effect of Changes of Cu on Q* C o =$2.00-$0.20=$1.80, C u =$0.20, F(Q*) =.9 17 Honeywell Condition Based Maintenance

18 Effect of Changes of Co on Q* C o =$1.00-$0.30=$.70, C u =$0.30, F(Q*).7 18 Honeywell Condition Based Maintenance

19 Implications Optimal Inventory Level is Strongly Dependent On - Mean (µ) -> Direct Linear Effect - Standard Deviation (σ) -> Direct Approximately Linear Effect - Overstock Cost (C o ) -> Inverse, Nearly Exponential Effect - Understock Cost (C u ) ->Direct, Nearly Exponential Effect C C + C u - Critical Ratio ( ) ->Direct, Nearly Exponential Effect o u 19 Honeywell Condition Based Maintenance

20 Additional Factors Factor Large Number of Non-Interchangeable Parts High Variance in Remaining Life Inability to Stock a Fractional Part Hierarchical Structure of Depots High Cost of Lost Functional Availability of Asset When Component Unavailable Long Delivery Cycle from US Expensive Parts High Cost of Transport to Forward Deploy Parts High Cost of Transport to Return Un-used Inventory from Forward Deployment Effect Produces N Simultaneous Optimal Inventory Problems Increases σ Increases µ Since Usually Round-Up Increases µ Since Fractional Round-Up Can Occur at Each Location Increase Cu Increases Cu and σ Increases Co Increases Co Increases Co 20 Honeywell Condition Based Maintenance

21 Opportunities for Improvement By PHM Factor Large Number of Non-Interchangeable Parts High Variance in Remaining Life Inability to Stock a Fractional Part Hierarchical Structure of Depots High Cost of Lost Functional Availability of Asset When Component Unavailable Long Delivery Cycle from US Expensive Parts High Cost of Transport to Forward Deploy Parts High Cost of Transport to Return Un-used Inventory from Forward Deployment PHM* / Other Opportunity Increase Interchangeability of Parts Use PHM to Prevent Damage to Parts Through Application of Timely Service. Use PHM to Predict Failures In Advance of Order Cycle. Use PHM to Improve Troubleshooting Accuracy. Use PHM to Allow Units to Share Spares. (Requires Prediction Window Great Enough to Allow Cross Load). Use PHM to Allow Depot Share Spares. (Requires Prediction Window Great Enough to Allow Cross Load). Increase Redundancy, Increase Interchangeability of Parts Use PHM to Allow Reach Back for Spares. (Requires Prediction Window Great Enough to Allow Reach Back). Use PHM to Reduce Total Number of Items Purchased due to Reduced Damage, Improved Troubleshooting Accuracy and Reduce Variation in Demand.. Use PHM to Allow Reach Back for Spares. (Requires Prediction Window Great Enough to Allow Reach Back). Use PHM to Reduce Total Amount of Parts Transported. 21 Honeywell Condition Based Maintenance

22 Challenges Diagnostic Errors Result In Additional Removals - Result in Unnecessary Removals During Troubleshooting - Significantly Reduces User s Confidence in System High Rate of False Alarms (aka False Positives) Will Quickly Offset Savings from Prognostics. - False Alarms Cause Additional Maintenance Actions - May Result in Unnecessary Removals - Reduces User s Confidence in System Missed Detections (aka False Negatives) Will - Missed Detections Result in Greater Problems After PHM Since Inventory Levels Would Have Been Reduced So Likelihood of Having Convenient Replacement is Much Lower. - Significantly Reduces Users Confidence in System. Take Away: Low Accuracy PHM May Be Worse Than No PHM. 22 Honeywell Condition Based Maintenance

23 Experience From 777 and 787 Central Maintenance Computer Development

24 Diagnostic System Overview [Evidence] Diagnostic System [Cause Likelihoods] The Evidence vector is a collection of binary condition indicators (system states, bucketized parameters, abnormality indicators, test results, operator complaints, etc) The Cause Likelihoods vector is a collection of possible causes with the likelihood for each indicating the relative likelihood that it is the cause of the evidence. Note: Evidence indicators are actually tri-state: Present, Absent, Unknown. 24 Honeywell Condition Based Maintenance

25 Diagnostic System Overview Model Based [Evidence] Diagnostic System [Cause Likelihoods] The Fault Model is a collection of objects and relations that are used by the diagnostic system so that the algorithms are independent of the particular system being diagnosed. [Fault Model] 25 Honeywell Condition Based Maintenance

26 Diagnostic Error Analysis Actual Failure Mode Actual System Actual Evidence + + Detected Evidence Aggregate Error Reasoning Errors + + Modeling Errors Measurement Errors Fault Model Cause Likelihoods + + Reasoning Algorithm 26 Honeywell Condition Based Maintenance

27 Diagnostic Error Analysis Reality Actual Failure Mode Actual System Actual Evidence + + Detected Evidence Distortion Aggregate Error Reasoning Errors + + Modeling Errors Measurement Errors Belief Fault Model Cause Likelihoods + + Reasoning Algorithm 27 Honeywell Condition Based Maintenance

28 Evaluation of Accuracy Question: How can you evaluate the accuracy of a diagnostic result? - If the Cause Likelihood Vector for a specified set of evidence were: Dead Battery:.50 Faulty Wiring:.30 Controller Fault.20 - On what basis could you assess that these were the correct values or in error? 28 Honeywell Condition Based Maintenance

29 Evaluation of Diagnostic Accuracy Question: How can you evaluate the accuracy of a diagnostic result? - If the Cause Likelihood Vector for a specified set of evidence were: Dead Battery:.50 Faulty Wiring:.30 Controller Fault.20 - On what basis could you assess that these were the correct values or in error? Answer 1: These likelihoods should be derived from the population of all simulated and/or real faults that produce all of the specified evidence (Correspondence). Answer 2: These likelihoods should represent the likelihood that the associated corrective action will in fact correct the defect (Effectiveness) Both answers are useful, but Answer 1 is more valuable since can be evaluated in advance of the deployment of the system. 29 Honeywell Condition Based Maintenance

30 Prognostic Error Analysis Reality Actual System Health Actual System Actual Evidence + + Detected Evidence Distortion Aggregate Error Reasoning Errors + + Modeling Errors Measurement Errors Belief Fault Model Cause Likelihoods Time To Failure + + Reasoning Algorithm 30 Honeywell Condition Based Maintenance

31 Evaluation of Prognostic Accuracy Question: How can you evaluate the accuracy of a prognostic result? - If the Cause Likelihood Vector for a specified set of evidence were: Dead Battery: Faulty Wiring: Controller Fault.50, 20 hrs,.30, 40 hrs,.20, 40 hrs - On what basis could you assess that these were the correct values or in error? Answer: These results should be derived from the population of all simulated and/or real degradation conditions that produce all of the specified evidence. System must determine if confidence is high enough to inform user based on degree of novelty in current situation compared to population model. 31 Honeywell Condition Based Maintenance

32 Implications of PHM Accuracy Analysis Of the Three Sources of PHM Error: - Measurement Error - Reasoning Error - Modeling Error Modeling Error will be the Source of Most Errors for the Foreseeable Future. Sophisticated Tools Sharing Data Trough Open Standard Will Be Needed to Address This Challenge. 32 Honeywell Condition Based Maintenance

33 Maintenance System Lessons Learned (pre-boeing 777) Earlier Maintenance Systems suffered from: - Poor Correlation between Pilot Observations and required Mechanic Actions - Human Usage Scenarios not adequately addressed - False, Misleading and Ambiguous Nuisance Messages - Lack of Built-In Test (BIT) consistency among Subsystems - Poor Handling of Power Transient Response - Optional Equipment not covered by Maintenance System - Slow turnaround of software rule updates did not keep up with aircraft design changes - Poor visibility into effects caused by software rule updates NUMEROUS SYSTEM INTEGRATION PROBLEMS 33 Honeywell Condition Based Maintenance

34 CMC Serves as an 'Airplane Doctor' Boeing 777 introduced the CMC fault-model approach CMC Monitors all aircraft Member Systems - Continually collects symptoms, during flight, from all the avionics boxes on the airplane - Diagnoses the real fault (i.e., the root cause) behind the symptoms - Correlates the fault with flight crew observations (alerts) - Informs the maintenance crew of the required repair action Nearly Nearly all all of of the the CMC CMC functionality is is controlled by by the the Fault Fault Model!!! Data Driven Functions Include: I/O, Nuisance Suppression, Inhibit Processing, Time Delay Processing, Cascade Removal, Consolidation, FDE Correlation, Maintenance Message Displays, Initiated Test Displays, Configuration Reporting 34 Honeywell Condition Based Maintenance

35 777 CMC Uses Tool to Aggregate System Models Previous Rule-Based Approach Interconnect Puzzle Piece Sub-System Behavior puzzle piece Expert System Engineer is asked to diagnose faulty LRU for thousands of symptom scenarios Scenario 1 Scenario 2 (If box 1 said.. and box 2 said.. then box 3 is bad) (If box 8 said.. and box 9 said.. then box 23 is bad) Software On-Board Unit Honeywell s Model-Based Approach Interconnect Puzzle Piece Sub-System Behavior puzzle piece Honeywell DCT Tool Diagnostic Model is Hierarchical Data Table CMC Each expert is asked to describe only his/her subsystem behavior Honeywell modeling tool fits the pieces together and generates a data table The data table is used by the CMC software to diagnose failures 35 Honeywell Condition Based Maintenance

36 Knowledge Management Approach to 777 / 787 CMC Problem Statement - Provide tools and processes to allow each of 100 system suppliers to model the failure modes, functional effects and detected symptoms for their portion of the aircraft - Provide tools and processes to allow Boeing to integrate all models into comprehensive, aircraft level model. - Model structure must account for all variations in interconnections between systems and for variations in ways that systems reported symptoms to the CMC - Model structure must provide economic solution to the problem of modeling redundant systems (since 90% of model content is the same between all installations of the redundant components). - Model structure must capture all data needed to support all of the functionality of the CMC 36 Honeywell Condition Based Maintenance

37 Aerospace Fault Model Development Process Platform Test Test Test on Simulation Test on Aircraft Record Results Submit Results Platform Integrator Import Systems Update Systems Update User Accounts Import ICD(s) Import FDEs) Review LRU Data Create / Update Aircraft Data Perform Analysis Generate Reports Audit Release ASCII LDI Create Binary LDI Export Data to Service Tools Export Data to Factory Export Data to Tech Pubs System / LRU Suppliers Import FMEA Data Define LRUs Define Fault Reports Define Isolation Tables Define Special Functions Define Screens Define Parametric Data Audit / Test Submit Update LRU Model Data Audit / Test Submit Simulate LRU / System Faults Record Results Submit Results Note: Symbol indicates data transfer to/from external system Honeywell Provided Tool Used By Integrator and Suppliers to Develop and Manage Fault Model. 37 Honeywell Condition Based Maintenance

38 Hierarchical Fault Model (Connectivity Based) Platform Model LRU 1 LRU 2 LRU 5 LRU 6 The LRU model is composed of four parts: - IO Definitions - Symptom Definitions - Failure Mode and Effect Definitions - Propagation Data LRU 4 LRU 3 The Platform Model is composed of five parts: - LRU Installation Definitions - Repair Instructions - Platform Level Signal Definitions - Platform Functional Dependency Data - IVHM Configuration Data - Data Collection Rules - Inhibit Data - Calculated Cascade Data - Calculated Time Delay Data I_1 I_2 LRU 4 Inputs LRU Reference Model Symptoms Failure Mode Propagation Outputs O_1 O_2 38 Honeywell Condition Based Maintenance

39 Fault Model Overview Function detectslossof Fault Report Document Reference has_document Detetcts suppresses Inhibit Condition invalidates Defines Cascade Path Symptom applicable_to Service Bulletin Signal causes produces Test defined_by affects causes Failure Mode has LRU IO Definition Circuit has repaired_by repaired_by Repair The fault model must be built and maintained through a rigorous knowledge management process. 39 Honeywell Condition Based Maintenance

40 Knowledge Management Approach to PHM Open System Tool Allows System / Component Supplier to Develop Fault Model. - This Approach Was Used on B777 and B787 Aircraft. Standard Model Exchange Schema Allows Integration Of Fault Models From Many Suppliers. - This Approach Was Used on FCS / PS-MRS Program. Approaches Can Be Combined to Address Specific Factors of Procurement Office, Platform Integrator, and System / Component Suppliers 40 Honeywell Condition Based Maintenance

41 Summary Logistic Costs Can Be Significantly Reduced If PHM Provides High Accuracy Diagnostic, Prognostic and Coordination Functions. Errors in PHM Functionality Significantly Reduce Its Value. Distributed Development of Diagnostic and Prognostic Models Through Rigorous Knowledge Management Process is An Important Enabler of High Accuracy PHM. 41 Honeywell Condition Based Maintenance