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Using 6-Sigma Experimental Design Tools in Product Improvement Testing MAESC May 11, 2005 Paul Babin, P.E., William Parker

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Using 6-Sigma Experimental Design Tools in Product Improvement Testing What is 6-Sigma? Experimental Design Rubber Plug Example Planning the Test Results – ANOVA Engineering Model Regression Analysis Synthesis of Models and Experiments

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What is 6-Sigma? 3.4 ppm 3.4 PPM

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MeasureDefineAnalyzeImprove EXECUTION Control Control the process to assure that important improvements are sustained. Define the key processes that affect customers. Analyze the data, converting it to insightful information. Improve the process to achieve the results desired. Measure the performance of key characteristics. 6-Sigma Process Improvement Methodology

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Comparing Six Sigma, Lean, TOC ref Dave Nave, Quality Progress, March 2002 ProgramSix SigmaLean ThinkingTheory of Constraints TheoryReduce variationRemove wasteManage constraints Application Guidelines 1. Define 2. Measure 3. Analyze 4. Improve 5. Control 1. Identify value 2. Identify value stream 3. Flow 4. Pull 5. Perfect 1. Identify constraint 2. Exploit constraint 3. Subordinate constraint 4. Elevate constraint 5. Repeat cycle FocusProblem focusedFlow FocusedSystem constraints

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6-SigmaTools by DMAIC Phase ref Implementing 6-Sigma, Breyfogle 2003 Define Project Selection Matrix Cost of Quality Project Charter Measure Key process output variables Financial Metrics Voice of the Customer Analyze Box Plots, Pareto Charts, Control Charts Scatter plots, Comparison Tests Regression Analysis ANOVA (Analysis of Variance) Improve Key process input variables DOE (Design of Experiments) Full Factorial DOEs 2 k Fractional Factorial DOEs Robust Designs Response Surface Methodology Improvement Recommendations Control Process Maps, SOPS, Failure Mode and Effects Analysis, Mistake Proofing Control Plan Change Management

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Experimental Design Statistical Methods that provide an investigator with a way to overcome the difficulties typically encountered including: Experimental Error (noise) Confusion of correlation with causation Complexity of the effects to be studies Adapted from Box, Hunter, and Hunter 1978

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Design of Experiments Process Response Experimental Error (Noise) Factors

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Using DOE in a 6-Sigma Project Select an appropriate Response Variable Continuous Variable (ratio level) Measurable Identify possible factors and interactions Select factors and factor levels Plan the experiment (treatment combinations) Conduct the experiment Analyze the Results Recommend Improvements (or further testing)

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Example : Plug DOE Response Variable: Holding Pressure Factors (and levels): Tube Size (5 sizes) Tube Wall (thick and thin) Plug Material (old & new) Temp (high & low) Full factorial design 40 treatment combinations (5x2x2x2)

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Running The Test Insert Plug and condition for 24 hours Slowly increase air pressure Note the pressure at which the plug just starts to move

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Running the Test

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ANOVA SourceDFSSMSFp Model72660.45380.0613.01<.0001 Error32934.6529.21 Total393595.10 SourceNparmDFSSFP Size441366.3511.69<.0001 Wall11313.6010.740.0025 Matl11980.1035.56<.0001 Temp110.400.0140.9076 R 2 = 0.74

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ANOVA SourceDFSSMSFp value Model72660.45380.0613.01<.0001 Error32934.6529.21 Total393595.10 SourceNparmDFSSFP value Size441366.3511.69<.0001 Wall11313.6010.740.0025 Matl11980.1035.56<.0001 Temp110.400.0140.9076 R 2 = 0.74

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What does that mean? Validated Test Method. Reduced (but not eliminated) noise Discriminate between important differences Factors explained 74% of the variation Temperature not important No Interactions

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Engineering Model Predictive Model Press Fit Concentric Model Response: Holding Pressure Variables: Coefficient of Friction Elastic Modulus & Poisson’s Ratio Amount of Compression Cross Sectional Area

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Regression Analysis of Engineering Model : Average Test Pressure Observed vs. Predicted

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Future Analysis – FEA models

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Comparing the Models Engineering Model Holding Pressure = Non- linear function of Amount of Compression Plug Wall thickness Coefficient of friction Young’s modulus Poisson’s ratio Plug length R 2 = 80% (using averages) Factorial Experiment Holding Pressure = b1 * Material + b2 * Size + b3 * Wall + error no temperature effect no interactions between factors R 2 = 74% But where do we get all the parameters to plug in? Experimentation!

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Synthesis Engineering Models Describe behavior based on physical properties Provides a precise predicted average value Factorial Experiment Describe experimental variation Determine important factors Validate Engr Model 6-Sigma Product Improvement Understand and Reduce Variation $$$

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References: Breyfogle, Forrest W. III, “Implementing Six Sigma – Smarter Solutions Using Statistical Methods, 2 nd Edition”, Wiley, 2003. Box, George E.P., William G. Hunter, J. Stuart Hunter, “Statistics for Experimenters – An Introduction to Design, Data Analysis, and Model Building”, Wiley, 1978. Nave, Dave, How to Compare Six Sigma, Lean and the Theory of Constraints. Quality Progress, March 2002. ASTM D 2990 – Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics. Brewer, Peter C., Jan E. Eighme, Using Six Sigma to Improve the Finance Function, Strategic Finance, May 2005.

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Questions?

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Extra Slides

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Test Methods ASTM D 2990 – Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics. Viscoelastic Creep Note 8 – Precision and Bias Attempts to develop a precision and bias statement for these test methods have not been successful…

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3 sigma = 99.73% 2700 ppm defective

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6 sigma = 99.999660% 3.4 ppm defective even with shift in mean

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Another 6-SigmaTool list ref Using Six Sigma to Improve the Finance Function, Brewer 2005 Define Surveys, CTQ Ranking Pareto Chart, Five Whys Technique Measure Company-Wide definition Guidelines Data Collection Plan & Sheets Sigma Calculation Prioritization Matrix Analyze Process Mapping, Value Added Analysis Bottleneck Analysis, Fishbone Diagram Outside Suggestions Deductive Reasoning and FMEA Pareto Chart, Histogram, Dot Plots, Regression Analysis Discussion, Voting Improve Brainstorming Outside Suggestions Voting Cost/Benefit Analysis Solution Prioritization Matrix Piloting Plan Control Standard Operating Procedures Project Library Control Chart Pareto Chart Balanced Scorecard Mistake Proofing

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