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1. Innovative Design for Six Sigma (DFSS) Approaches to Test and Evaluation Dr. Mark J. Kiemele Air Academy Associates Tutorial 21st Annual National Test & Evaluation Forum National Defense Industrial Association Air Academy Charlotte, NC Associates March 7, 2005 Copyright 2005 2. Introductions Name Job Title/Duties - Deployment Leader, Champion, MBB, BB, GB, manager, consultant, etc. Expectations Air Academy Associates Copyright 2005 1 3. Warm-Up Exercise Goal: full concentration on the subject at hand Eliminate extraneous issues that could inhibit that Write down the top issue on a plain sheet of paper Jettison this issue by doing the following: - Design a paper airplane that will help you deposit this issue in the waste basket. - Launch your paper airplane at the waste basket from your seating area. You may stand or even move around to launch if you wish. Air Academy Associates - Goal is to put the issue in the waste basket, which is Copyright 2005 obviously symbolic of putting the issue away. 2 4. Agenda A Design for Six Sigma (DFSS) Primer Testing at 2 Levels and Gray Code Sequencing Testing at More Than 2 Levels (Central Composite Designs) Break Monte Carlo Simulation, Robust Design, and Tolerance Allocation High Throughput Testing Multidiscipline Design Optimization with Latin Air Academy Hypercube Sampling Associates Copyright 2005 3 5. Six Sigma Defined Originally: Metric Based on the Statistical Measure Called Standard Deviation Expanded To: WORLD CLASS QUALITY Providing a Low High Spec Spec BETTER product or service, FASTER, and at a LOWER COST than our competition. VARIATION is the enemy! Air Academy Associates "Always know the language of the enemy." Copyright 2005 4 6. Graphical Meaning of a Distribution y (measure of performance) 130 140 150 160 170 Air Academy Associates Copyright 2005 5 7. Graphical Meaning of y y (measure of performance) 130 140 150 160 170 y 153 Air Academy Associates Copyright 2005 6 8. Graphical Meaning of Points of Inflection Point of Inflection Point of Inflection y (measure of performance) 130 140 150 160 170 y 153 Air Academy Associates Copyright 2005 7 9. Graphical Meaning of = distance from the center of the distribution to a point of inflection Point of Inflection For this example, 7 = 160 - 153 y (measure of performance) 130 140 150 160 170 y 153 Air Academy Associates Copyright 2005 8 10. Graphical View of Variation and Six Sigma Performance The Sigma Capability of a process performance measure compares the Voice of the Process with the Voice of the Customer, and it is defined as follows: The number of Sigmas between the center of a process performance measure distribution and the nearest specification limit Lower Upper 3 Process Centered Specification Specification Process is WIDER Limit 3 Process Limit than the specifications, causing waste and Determined by Determined by cost of poor quality the customer the customer -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 WASTE 6 Process WASTE 6 Process Centered Process FITS well within the specifications, so even if the process shifts, the values fall Air Academy well within Associates tolerances Copyright -6 -5 -4 -3 -2 -1 0 +1 +2 +3 +4 +5 +6 2005 9 11. Why Six Sigma? N (Simplify) NE E (Perfect) OVERALL YIELD vs SIGMA (Distribution Shifted 1.5 ) # of Parts 3 4 5 6 (Steps) 1 93.32% 99.379% 99.9767% 99.99966% 7 61.63 95.733 99.839 99.9976 10 50.08 93.96 99.768 99.9966 20 25.08 88.29 99.536 99.9932 40 6.29 77.94 99.074 99.9864 60 1.58 68.81 98.614 99.9796 80 0.40 60.75 98.156 99.9728 100 0.10 53.64 97.70 99.966 150 --- 39.38 96.61 99.949 200 --- 28.77 95.45 99.932 300 --- 15.43 93.26 99.898 400 --- 8.28 91.11 99.864 500 --- 4.44 89.02 99.830 600 --- 2.38 86.97 99.796 700 --- 1.28 84.97 99.762 800 --- 0.69 83.02 99.729 900 --- 0.37 81.11 99.695 1000 --- 0.20 79.24 99.661 1200 --- 0.06 75.88 99.593 3000 --- --- 50.15 98.985 17000 --- --- 1.91 94.384 Air 38000 --- --- 0.01 87.880 Academy 70000 78.820 Associates 150000 Use for 60.000 Copyright Benchmarking Source: Six Sigma RESEARCH INSTITUTE Motorola University Motorola, Inc. 2005 10 12. How Process Capability Impacts Cycle Time and Resource Allocation Step X Step Y LS US LS US .. Desired End Desired End Start No Defect No Defect State State Defect Defect Defect Defect Test Test Test Test Analyze Analyze Analyze * Analyze * Fix Fix Fix Fix Every Time a Defect is Created During a Process (Step), it Takes Additional Cycle Time to Test, Analyze, and Fix. Air * These Non-Value Added Activities Typically Require Additional Floor Space, Capital Academy Associates Equipment, Material, and People. Copyright 2005 11 13. Is it Six Sigma at All Cost? Total Cost Typical Six Sigma Barrier DFSS Optimal Point Air Academy Associates 2 3 4 5 6 7 Copyright 2005 Sigma Rating 12 14. Food for Thought... The systems and products that deliver value to our customers are perfectly designed to achieve the results we are getting today. Air Academy Associates Copyright 2005 13 15. DFSS What is it? Design For Six Sigma is: A methodology for designing new products and/or processes. A methodology for re-designing existing products and/or processes. A way to implement the Six Sigma methodology as early in the product or service life cycle as possible. A way to exceed customer expectations. A way to gain market share. A strategy toward extraordinary ROI. Air Academy Associates Copyright 2005 14 16. Why DFSS "Classic" Six Sigma focuses here 1000 Relative Cost to Make a Design Change 100 DFSS focuses here 10 1 Research Design Development Production Product Stage Air Academy "Design in" quality when costs are lowest "Design in" quality when costs are lowest Associates Copyright Show customers Six Sigma products right from the start Show customers Six Sigma products right from the start 2005 15 17. The Opportunity of DFSS Resources Revenue Required Generated DFSS Vision: Predictive Design Revenue w/ DFSS Revenue w/o DFSS Launch Launch Time Early problem identification; solution when costs low Pre-DFSS: Reactive Design Faster market entry: earlier revenue stream, longer patent coverage Unhappy customers Lower total development cost Unplanned resource drain Robust product at market entry: delighted customers Skyrocketing costs Resources available for next game-changer Next product compromised Air Academy Associates Copyright Upfront investment is most effective and efficient Upfront investment is most effective and efficient 2005 Show customers 6P products right from the start Show customers 6P products right from the start 16 18. The DFSS Process: IDOV Market Assessment / ID New Markets Competitive Assessment / Benchmarking Results Introduction to DFSS Prioritization of Ideas Strategic Alignment Prioritized Customer Requirements Keeping Score Identify Prioritized CTC's House of Quality #1 Voice of Customer Initial Performance Scorecard Validate Customer Needs Systems Engineering and Concept Development Requirements Flowdown Preliminary Design Risk Assessment Prioritized Product Design Characteristics House of Quality #2 Design Performance/Process Scorecard Transfer Function Transfer Function(s) Design for Robust Process Development Performance Assess Manufacturability Process Capability Studies Tolerance Allocation Reliability Studies Capability Flowup Optimize Design for Manufacturability Optimal Design Tolerances on X's Complete Scorecard Product Capability Prediction Virtual Prototype No Prototypes OK Process Validation Yes Product Validation Test and Validate Capable Product and Process Air Sensitivity Analysis and Control Plans Academy Validate Commercialization Support Associates No OK Copyright Yes 2005 * The IDOV four-phase DFSS process originated with Dr. Celebrate Norm Kuchar at GE CRD and is used with permission. 17 19. DFSS Tools Identify Design Optimize Validate Project Charter Assign Specifications Histogram Sensitivity Analysis Strategic Plan to CTCs Distributional Analysis Gap Analysis Cross-Functional Team Customer Interviews Empirical Data Distribution FMEA Voice of the Customer Formulate Design Concepts Expected Value Analysis (EVA) Fault Tree Analysis Benchmarking Pugh Concept Generation Adding Noise to EVA Control Plan KANOs Model TRIZ or ASIT Non-Normal Output Distributions PF/CE/CNX/SOP Questionnaires FMEA Design of Experiments Run/Control Charts Focus Groups Fault Tree Analysis Multiple Response Optimization Mistake Proofing Interviews Brainstorming Robust Design Development MSA Internet Search QFD Using S-hat Model Reaction Plan Historical Data Analysis Scorecard Using Interaction Plots High Throughput Testing Design of Experiments Transfer Function Using Contour Plots Quality Function Deployment Design of Experiments Parameter Design Pairwise Comparison Deterministic Simulators Tolerance Allocation Analytical Hierarchy Process Discrete Event Simulation Design For Manufacturability and Assembly Performance Scorecard Confidence Intervals Mistake Proofing Flow Charts Hypothesis Testing Product Capability Prediction FMEA MSA Part, Process, and SW Scorecard Air Visualization Computer Aided Design Risk Assessment Academy Computer Aided Engineering Reliability Associates Multidisciplinary Design Optimization (MDO) Copyright 2005 18 20. Systems Engineering Main System Automobile Sub System Drive Train Body Electrical Assemblies Engine Transmission Parts Spark Plugs Valves Injectors Complex products may require the "Divide and Conquer" approach. Flow the system requirements down and roll the capability up. Air Academy Associates System Engineers are the masters of the scorecard and make Copyright tradeoff decisions. 2005 19 21. Flowing the Requirements Down Functional Req. (CTC's) Customer Req. Customer Prod. Design Expectations House of Characteristics Quality Functional Req. #1 House of Mfg. Process (CTC's) Characteristics Quality Characteristics Prod. Design #2 House of Mfg. Process Control Performance Quality Characteristics Mfg. Process CTC's #3 House of Product Quality Design CTC's #4 Process Design CTC's Mfg. Process Control Marketing Design Engineering Mfg. Engineering Manufacturing Features Performance Manufacturability SPC Quality Reliability Cost Process Capability Air Performance Cost Academy Cost Associates Copyright DFSS 2005 Six Sigma 20 22. Transfer Functions X1 Parameters or Factors X2 Process y (CTC) that Influence the CTC X3 y = f1 (x1, x2, x3) s = f2 (x1, x2, x3) Where does the transfer function come from? Exact transfer Function Approximations Air - DOE Academy Associates - Historical Data Analysis Copyright 2005 - Simulation 21 23. Exact Transfer Function Engineering Relationships - V = IR - F = ma R1 The equation for the impedance (Z) through this circuit is defined by: R1 R 2 Z= R2 R1 + R 2 x The equation for magnetic force at a distance X from the center of a solenoid is: l N .5l + x .5l x H= + 2 2l r 2 + (.5l + x )2 r + (.5l x )2 r Where N: total number of turns of wire in the solenoid : current in the wire, in amperes Air r: radius of helix (solenoid), in cm Academy Associates l: length of the helix (solenoid), in cm Copyright x: distance from center of helix (solenoid), in cm 2005 H: magnetizing force, in amperes per centimeter 22 24. What Is a Designed Experiment? Purposeful changes of the inputs (factors) in order to observe corresponding changes in the output (response). X1 Y1 X2 Inputs X3 PROCESS Y2 Outputs X4 . . . . . . Run X1 X2 X3 X4 Y1 Y2 ...... Y SY 1 2 3 Air . Academy Associates . Copyright 2005 23 25. DOE Helps Determine How Inputs Affect Outputs i) Factor A affects the average A1 A2 y ii) Factor B affects the standard deviation B1 B2 y iii) Factor C affects the average and the standard deviation C1 C2 y Air iv) Factor D has no effect Academy Associates D1 = D2 Copyright 2005 y 24 26. Catapulting Statistics Into Engineering Curricula Air Academy Associates Statapult Copyright 2005 25 27. Catapulting Statistics Into Engineering Curricula (cont.) y mg B F D 0 0 x d Mg 0 R 0x Air 0y Academy Associates Copyright 2005 26 28. Formulas D rF sin I0 && = rF F( ) sin cos (MgrG + mg rB ) sin tan = , d + rF cos 1 &2 I0 = rF F( ) sin cos d (MgrG + mg rB ) (sin sin 0 ) 2 0 1 1 &2 I0 1 = rF F( ) sin cos d (MgrG + mg rB ) (sin 1 sin 0 ). 2 0 1 1 2 x = v B cos 1 t rB cos 1 y = rB sin 1 + v B sin 1 t gt . 2 2 2 2 g (R + rB cos 1) 2 rB sin 1 + (R + rB cos 1) tan 1 = 0. 2 2 2VB cos2 1 2 gI0 (R + rB cos 1)2 4rB cos2 1 rB sin 1 + (R + rB cos 1) tan 1 2 2 Air 1 Academy Associates = rF F( ) sin cos d (MgrG + mg rB )(sin 1 sin 0 ). Copyright 0 2005 27 29. Statapult Exercise (DOE demonstration) Actual Coded Factors Response Values Factors Run A B A B AB Y1 Y2 Y S 1 2 3 4 Avg Y= Avg + Air Academy Associates Copyright 2005 28 30. Minimizing the # of Factor Changes (GRAY CODE SEQUENCE) Problem: If changing factor settings is time consuming and/or expensive, using a Gray Code sequence to determine the sequence of runs may be useful. A Gray Code sequence orders the runs so that only 1 factor setting changes between runs and the most difficult to change factors are changed less frequently. 16-Run Design Gray Code by Run # Run A B C D 1 Cycling through the runs from top to 1 - - - - 2 2 - - - + bottom (or vice versa) will produce 15 4 3 - - + - changes: 3 4 - - + + D will be changed 8 times. 7 5 - + - - C will be changed 4 times. 8 6 - + - + B will be changed 2 times. 7 - + + - 6 A will be changed 1 time. 8 - + + + 5 9 + - - - 13 10 + - - + 14 Thus, the most difficult (or expensive) to 11 + - + - 16 change factors should be assigned to A, 12 + - + + 15 B, C, D, respectively. 13 + + - - 11 14 + + - + Air 15 + + + - 12 Academy Associates 16 + + + + 10 9 Copyright 2005 29 31. Test Sequence Generator A D D C C 9 1 10 2 D 12 4 D 11 3 B B 15 7 D 16 8 D 14 6 13 5 C C D D Air A Academy Associates Copyright Gray Code Sequence Generator (Wheel) 2005 by Run Number for 16 Runs and 4 Factors 30 32. Simple DOE Augmentation to Possibly Reduce the Number of Tests FACTORS OF FACTORS OF SECONDARY PRIMARY INTEREST INTEREST A B C D TRIAL 1 - - - - TRIAL 2 - - - + TRIAL 3 - - + - TRIAL 4 - - + + TRIAL 5 - + - - TRIAL 6 - + - + TRIAL 7 - + + - TRIAL 8 - + + + TRIAL 9 + - - - TRIAL 10 + - - + TRIAL 11 + - + - TRIAL 12 + - + + TRIAL 13 + + - - Air Academy TRIAL 14 + + - + Associates TRIAL 15 + + + - Copyright TRIAL 16 + + + + 2005 31 33. Building a Screening Design L1 2 Design Run 1 2 3 4 5 6 7 8 9 10 11 1 - - - - - - - - - - - 2 - - - - - + + + + + + 3 - - + + + - - - + + + 4 - + - + + - + + - - + 5 - + + - + + - + - + - 6 - + + + - + + - + - - 7 + - + + - - + + - + - 8 + - + - + + + - - - + 9 + - - + + + - + + - - 10 + + + - - - - + + - + 11 + + - + - + - - - + + 12 + + - - + - + - + + - Air Academy Associates Copyright 2005 32 34. KISS Guidelines for Choosing an Experimental Design KISS - Keep It Simple Statistically START PF Process flow diagram Steve Schmidt inputs Source: Mark Kiemele STATEMENT CE Cause-and-effect diagram Cass Grandone of the outputs PROBLEM & C Inputs on cause-and-effect to be held constant OBJECTIVE N Inputs on cause-and-effect that are noise or uncontrolled DETERMINE WHAT X Inputs (factors) on cause-and-effect identified for experimentation TO MEASURE & COMPLETE SOPs Standard operating procedures to insure all Cs are held constant PF/CE/CNX/SOPs and process flow is complied with HOW 2 3 TYPE QUANTITATIVE ONLY MANY LEVELS of FOR EACH FACTORS? FACTOR? NOT ALL HOW QUANTITATIVE MANY (i.e., at least FACTORS 1 Qualitative) 4 K 7 MODELING K 4 (K)? 6 K 11 6 K 8 or HOW K 3 SCREENING? MANY K=5 FACTORS Screening (K)? 6 K 7 Modeling K 5 12 Run 16 Run FULL FACTORIAL 25-1 PLACKETT-BURMAN FRACTIONAL K = 2 nreps 9 FRACTION TAGUCHI L18 CENTRAL COMPOSITE or TAGUCHI L12 FACTORIAL FULL FACTORIAL K = 3 nreps 5 nreps 3 SCREENING or SCREENING nreps 3 K = 2 nreps 7 K = 4 nreps 3 (also includes One BOX-BEHNKEN DESIGN nreps 4 K = 3 nreps 3 Air 2-level Factor) K = 2 nreps 9 (CCD) Academy nreps 4 K = 3 nreps 5 (CCD or BB) Associates NOTE 1: Sample size (nreps) is for 95% confidence in s and 99.99% confidence in y. K = 4 nreps 3 (CCD or BB) NOTE 2: (nreps/2) will provide 75% confidence in s and 95% confidence in y. K = 5 nreps 3 (CCD) Copyright NOTE 3: The 12 Run Plackett-Burman or L12 is very sensitive to large numbers of interactions. If this is the case, you would be 2005 better off using the 16 Run Fractional Factorial or a smaller number of variables in 2 or more full factorial experiments. NOTE 4: For more complete 2-level design options, see next page. 33 35. Value Delivery: Reducing Time to Market for New Technologies INPUT OUTPUT Pitch