Presentation on theme: "ESD Systems Engineering"— Presentation transcript:
1ESD.33 -- Systems Engineering Session #13Robust Design
2Plan for the Session Taguchi’s Quality Philosophy – Taguchi_Clausing Robust Quality.pdf• Implementing Robust Design– Ulrich_Eppinger Robust Design.pdf• Research topics– Comparing effectiveness of RD methods– Computer aided RD– Robustness invention• Next steps
3Robust Design – Improve the quality of a product (noise factors) A set of design methods that– Improve the quality of a product– Without eliminating the sources of variation(noise factors)– By minimizing sensitivity to noise factors– Most often through parameter design
4Engineering Tolerances • Tolerance --The total amount by which aspecified dimension is permitted to vary(ANSI Y14.5M)Every componentwithin spec addsto the yield (Y)
14System Verification Test • AFTER maximizing robustness• Make a system prototype• Get a benchmark (e.g., a goodcompetitor’s product)• Subject BOTH to the same harshconditions
15Taguchi’s Quality Imperatives • Quality losses result from poor design• Signal to noise ratios should be improved• Expose your system to noises systematically• Two step process – reduce variance firstTHEN get on target• Tolerance design – select processes basedon total cost (manufacturing cost AND quality)• Robustness in the field / robustness in thefactory
16Plan for the Session • Taguchi’s Quality Philosophy – Taguchi_Clausing Robust Quality.pdfImplementing Robust Design– Ulrich_Eppinger Robust Design.pdf• Research topics– Comparing effectiveness of RD methods– Computer aided RD– Robustness invention• Next steps
17Robust Design Process • Identify Control Factors, Noise Factors, and Performance Metrics• Formulate an objective function• Develop an experimental plan• Run the experiment• Conduct the analysis• Select and confirm factor setpoints• Reflect and repeat
18The “P” Diagram There are probably lots of noise factors, but a few are usuallydominantThere are usually more control factors than responses
19Full Factorial Experiments For example, if only two factors (A and B)are exploredThis is called afull factorial designpk=32The number ofexperimentsquickly becomesuntenable
20k(p-1)+1=9 Orthogonal Array requires only But main effects and Explore the effects of ALL 4 factors in abalanced fashionrequires onlyk(p-1)+1=9But main effects andinteractions areconfounded
21Outer Array Induce the same noise factor levels for each row in a balanced manner
22Compounding NoiseIf the physics are understood qualitatively, worst case combinations may be identified a priori
23Signal to Noise Ratio Adjustment PERMIA (two-step optimization) PERformance Measure Independent ofAdjustment PERMIA (two-step optimization)
25What is an Interaction?If I carry out this experiment, I will find that:
26Robust Design Process • Identify Control Factors, Noise Factors, and Performance Metrics• Formulate an objective function• Develop an experimental plan• Run the experiment• Conduct the analysis• Select and confirm factor setpoints• Reflect and repeat
27Plan for the Session • Taguchi’s Quality Philosophy – Taguchi_Clausing Robust Quality.pdf• Implementing Robust Design– Ulrich_Eppinger Robust Design.pdfResearch topics– Comparing effectiveness of RD methods– Computer aided RD– Robustness invention• Next steps
28Robust Design References • Phadke, Madhav S., 1989, QualityEngineering Using Robust DesignPrentice Hall, Englewood Cliffs, 1989.• Logothetis and Wynn, Quality ThroughDesign, Oxford Series on AdvancedManufacturing, 1994.• Wu and Hamada, 2000, Experiments:Planning, Analysis and ParameterDesign Optimization, Wiley & Sons,Inc., NY.
29Single Arrays Single arrays achieve improved run size economy (or provide advantages in resolving selected effects)Selection guided by “effect ordering principle”• “…those with a larger number of clear control-by-noiseinteractions, clear control main effects, clear noise maineffects, and clear control-by-control interactions arejudged to be good arrays.”• “Some of the single arrays … are uniformly better thancorresponding cross arrays in terms of the number ofclear main effects and two factor interactions”Wu, C. F. J, and H., M. Hamada, 2000, Experiments: Planning Analysis,and Parameter Design Optimization, John Wiley & Sons, New York.
30Comparing Crossed & Single Arrays 32 runsAll control factor maineffects aliased with CXCAll noise main effectsestimable21 CxN interactionsclear of 2ficlear of CxCxCclear of NxNxN32 runsAll control factor maineffects clear of 2fiAll noise main effectsestimable14 CxN interactionsclear of 2fi
31HierarchyIn Robust Design, control by noise interactions are key!
32Inheritance • Two-factor interactions are most likely when both participatingfactors (parents?) arestrong• Two-way interactionsare least likely whenneither parent is strong• And so on
33A Model of Interactions Chipman, H., M. Hamada, and C. F. J. Wu, 2001, “A Bayesian Variable Selection Approach forAnalyzing Designed Experiments with Complex Aliasing”, Technometrics 39(4)
34Fitting the Model to Data • Collect published full factorial data on variousengineering systems– More than data 100 sets collected so far• Use Lenth method to sort “active” and“inactive” effects• Estimate the probabilities in the model• Use other free parameters to make model pdffit the data pdf
36Robust Design Method Evaluation Approach 1. Instantiate models of multiple “engineeringsystems”2. For each system, simulate different robustdesign methods3. For each system/method pair, perform aconfirmation experiment4. Analyze the dataFrey, D. D., and X. Li, 2004, “Validating Robust Design Methods, accepted forASME Design Engineering Technical Conference, September 28 - October 2, SaltLake City, UT
37Results The single array is extremely effective if the typical modeling assumptions ofDOE hold
38Results The single array is terribly ineffective if the more realistic assumptions aremade
39effective than single arrays ResultsTaguchi’s crossed arrays are moreeffective than single arrays
40A Comparison of Taguchi's Product Array and the Combined Array in Robust Parameter Design We have run an experiment where we have doneboth designs simultaneously (product andcombined). In our experiment, we found that theproduct array performed better for theidentification of effects on the variance. Anexplanation for this might be that the combinedarray relies too much on the factor sparsityassumption.Joachim Kunert, Universitaet DortmundThe Eleventh Annual Spring Research Conference (SRC) on Statistics in Industryand Technology will be held May 19-21, 2004.
41Results An adaptive approach is quite effective if the more realistic assumptions aremade
42Results An adaptive approach is a solid choice (among the fast/frugal set) no matter whatmodeling assumptions are made
49Continuous-Stirred Tank Reactor Objective is to generate chemical species B at a rateof 60 mol/minAdapted from Kalagnanam and Diwekar, 1997, “An Efficient SamplingTechnique for Off-Line Quality Control”, Technometrics (39 (3)
50Comparing HSS and Quadrature Hammersley SequenceRequired ~ 150 points1% accuracy σ2σ2 from 1,638 to 232Nominally on targetMean 15% off targetQuadratureUsed 25 points0.3% accuracy in μ9% accuracy in (y-60)2 farfrom optimum0.8% accuracy in (y-60)2near to optimumBetter optimum, on targetand slightly lower varianceE(L(y)) =
51Plan for the Session • Taguchi’s Quality Philosophy – Taguchi_Clausing Robust Quality.pdf• Implementing Robust Design– Ulrich_Eppinger Robust Design.pdf• Research topics– Comparing effectiveness of RD methods– Computer aided RDRobustness invention• Next steps
53Harrison’s “H1” • Longitude Act of 1714 promises £20,000 • Accurate nauticaltimekeeping was onepossible key• But chronometerswere not robust to theshipboardenvironment• Harrison won throughrobust design!
54Example -- A Pendulum Robust to Temperature Variations • Period of the swing is affected bylength• Length is affected by temperature• Consistency is a key to accuratetimekeeping• Using materials with different thermalexpansion coefficients, the length canbe made insensitive to temp
55Defining “Robustness Invention” • A “robustness invention” is a technicalor design innovation whose primarypurpose is to make performance moreconsistent despite the influence of noisefactors• The patent summary and prior artsections usually provide clues
57Plan for the Session • Taguchi’s Quality Philosophy – Taguchi_Clausing Robust Quality.pdf• Implementing Robust Design– Ulrich_Eppinger Robust Design.pdf• Research topics– Comparing effectiveness of RD methods– Computer aided RD– Robustness inventionNext steps
58Next Steps • No HW • BUT, you should begin preparing for exam – Supplemental notes Clausing_TRIZ.pdf– When should exam go out?• See you at Thursday’s session testable– On the topic “Extreme Programming”– 8:30AM Thursday, 22 July• Reading assignment for Thursday– Beck_Extreme Programming.pdf– Williams_Pair Programming.pdf