MIXTURE DESIGN OF EXPERIMENTS USING CUSTOM DOE
MIXTURE DESIGN OF EXPERIMENTSUSING CUSTOM DOE PLATFORMMastering JMP Webcast October 26, 2017Tom DonnellySr. Systems EngineerJMP Federal Government TeamCopyright 2013, SAS Institute Inc. All rights reserved.
WHY USE DOE? QUICKER ANSWERS,LOWER COSTS,SOLVE BIGGER PROBLEMS,MAKE MORE MONEY!More rapidly answer “what if?” questionsDo sensitivity and trade-space analysisOptimize across multiple responsesBy running efficient subsets of all possible combinations, one can –for the same resources and constraints – solve bigger problemsBy running sequences of designs one can be as cost effective aspossible & run no more trials than are needed to get a useful answerSAME HOLDS TRUE FOR MIXTURE DOECopyright 2013, SAS Institute Inc. All rights reserved.
AGENDA Do trade-space analysis using models fit to a mixture DOE What makes mixture factors (components) and formulation DOE different? Several Examples Simple three-component designs using Custom DOE platform“Make Designs Fit the Problem – NOT Make Problems Fit the Designs!” Five-component mixture DOE with 3 constraints and response data (revisited) PDF – Ten-factor 6 mixture, 2 continuous, 1 categorical and 1 block Use constraints to define “mixtures within mixture”Can I find a 3-component blend that’s nearly as good as a 7-component blend?Technically Speaking – Optimizing Performance of a Multi-Layer Packaging Film “Real-world” several type of factorsAdditional constraints including holding some of mixture constantPDF – Seven-component mixture DOE with 5 and 7 constraints Visualizing process in Fit Model platformUse transformation to prevent physically impossible predictionsLayer thickness expressed as proportions that sum to one the mixture constraintCan I trade-off thickness and layer resin concentration to target 2 performance metrics & minimize a third?Computational Chemistry - Space-Filling Mixture DesignUS Army explosive formulation of “Bread.” Presented last week at JMP Discovery Summit 2017, St. Louis, MO, USA Copyright 2013, SAS Institute Inc. All rights reserved.
NEED TO PREDICTWANT TO MAKE INFORMED BUSINESS DECISIONSHARDNESS ANDTRADING OFF PRODUCT PERFORMANCE AND COSTCOST OF PLASTICWhat formulationsyield a Shore Ahardness of 50?What do theseformulations cost?Can I trade-offhardness and cost?Copyright 2013, SAS Institute Inc. All rights reserved.
MODEL OPTIMIZATIONSUGGESTS LOWERCOST IS POSSIBLEDOES THAT MAKE SENSE?DOES DATA SUPPORT IT?RUN CHECKPOINTS THERE.Copyright 2013, SAS Institute Inc. All rights reserved.
REAL-WORLD DESIGNISSUES ADDRESSED BYCUSTOM DOE PLATFORM “Make Designs Fit the Problem –NOT Make Problems Fit the Designs!”Work with these different kinds of control variables/factors:»Continuous/quantitative? (Finely adjustable like temperature, speed, force)»Categorical/qualitative? (Comes in types, like material rubber, polycarbonate, steel withmixed # of levels; 3 chemical agents, 4 decontaminants, 8 coupon materials )»Mixture/formulation? (Blend different amounts of ingredients and the processperformance is dependent on the proportions more than on the amounts)»Blocking? (e.g. “lots” of the same raw materials, multiple “same” machines, samples getprocessed in “groups” – like “eight in a tray,” run tests over multiple days – i.e. variables forwhich there shouldn’t be a causal effect Work with combinations of these four kinds of variables? Certain combinations cannot be run? (too costly, unsafe, breaks the process,subject matter experts say to avoid as “impractical.”) Use constraints. Certain factors are hard-to-change (temperature takes a day to stabilize) Would like to add onto existing trials? (really expensive/time consuming to run)Copyright 2013, SAS Institute Inc. All rights reserved.
MIXTURESIMPLE MIXTURE – MAKING SALAD DRESSINGVARIABLES Relative proportions offactors or components is moreimportant than actual quantityThree liquid components Oil, Water, and Vinegar8 oz. in Cruet vs. 4 gal. in Jug5 oz. “O”1 oz. “W”2 oz. “V” 5/81/81/4To study these mixturecomponents in a DOE useranges that are proportions:O: 0.500 to 0.750W: 0.000 to 0.250V: 0.125 to 0.375 320 oz.64 oz.128 oz.(½ to ¾)(0 to ¼)(⅛ to ⅜)Sum of proportionsconstrained to equal 1.–– O ––100.0%–– O –––– W –––– V ––37.5%25.0%–– W –––– V ––0%1 O W V so therefore W 1 – (O V), O 1 – (V W), & V 1 – (O W)Copyright 2013, SAS Institute Inc. All rights reserved.
INCREASE IN PROPORTION IS FROM BASE TO VERTEXFULL RANGE: 0 TO 1READING LEFT:EQUAL WIDTH RANGES: 0.125TERNARY PLOTS RIGHT:0.00Water0.2510.75 OilOil00.500WaterVinegar1 01Ternary plot is constrained so that if one locates where 2 of the 3coordinates intersect, the third coordinate is already determined.If Oil 0.6 and Vinegar 0.3, then Water 1 – (0.6 0.3) 0.1 (See )Copyright 2013, SAS Institute Inc. All rights reserved.0.375 Vinegar 0.125
SIX DESIGNS: Left:TOP: NO CONSTRAINTS Middle:BOTTOM: 2 CONSTRAINTSRight:Full Range: 0 to 1Equal width proportion: 0.125 about nominalEqual %change: 10% of nominalO/V 3/1O/V 2/1Copyright 2013, SAS Institute Inc. All rights reserved.
INEQUALITYCONSTRAINTALGEBRAExpress constraints as proportions2. Clear fractions (note keeping unit multiplier)3. Bring all factors to left side of inequality sign4. Fill in boxes with coefficients and select or 1.Oil/Vinegar 3/11*Oil 3*Vinegar1*Oil - 3*Vinegar 0andandandOil/Vinegar 2/11*Oil 2*Vinegar1*Oil - 2*Vinegar 0NOTE: Factors not in constraint get multiplied by zeroCopyright 2013, SAS Institute Inc. All rights reserved.
SIX DESIGNS: Left:TOP: 0 TO 1 RANGEBOTTOM: EQUAL WIDTH Middle: 0.125 ABOUT NOMINAL Right:Main Effects Model – 1st orderInteraction Quadratic model! – 2nd OrderScheffé Special Cubic model – 3rd OrderCopyright 2013, SAS Institute Inc. All rights reserved.
MODELCOMPLEXITYLeft:Middle:Right:Main Effects Model – 1st orderInteraction Quadratic model! – 2nd OrderScheffé Special Cubic model – 3rd Order1st order for screening – finding the critical few 2nd order for prediction and optimization 3rd order when 2nd order proves inadequate for prediction (lack-of-fit) NOTE: For low numbers of components one might consider making a designto support a 3rd order model but analyze first with 2nd order modelCopyright 2013, SAS Institute Inc. All rights reserved.
MODELCOMPLEXITYLeft:Middle:Right:Linear Blending* – 1st orderNonlinear Blending* – 2nd OrderVery Nonlinear Blending – 3rd OrderLinear (additive) blending – need only pure component response values Synergistic blending* – improvement in response exceeds additive prediction Antagonistic blending* – improvement in response is less than additive prediction *From Ron Snee’s JMP Explorers Event on DOE Strategies for Accelerating Formulation DevelopmentCopyright 2013, SAS Institute Inc. All rights reserved.
MAKE THIS DESIGNBROADEN CONSTRAINT WINDOW ON RATIO OF OIL/VINEGARFROM 2 O/V 3 TO 1.5 O/V 4O:V:W:(½ to ¾)(⅛ to ⅜)(0 to ¼)0.500 to 0.7500.125 to 0.3750.000 to 0.250Use a 2nd order modelO/V 4/1O/V 1.5/1Custom Design picks threedarker points each twice –minimizing predictionvarianceCopyright 2013, SAS Institute Inc. All rights reserved.
AGENDA Do trade-space analysis using models fit to a mixture DOE What makes mixture factors (components) and formulation DOE different? Several Examples Simple three-component designs using Custom DOE platform“Make Designs Fit the Problem – NOT Make Problems Fit the Designs!” Five-component mixture DOE with 3 constraints and response data (revisited) PDF – Ten-factor 6 mixture, 2 continuous, 1 categorical and 1 block Use constraints to define “mixtures within mixture”Can I find a 3-component blend that’s nearly as good as a 7-component blend?Technically Speaking – Optimizing Performance of a Multi-Layer Packaging Film “Real-world” several type of factorsAdditional constraints including holding some of mixture constantPDF – Seven-component mixture DOE with 5 and 7 constraints Visualizing process in Fit Model platformUse transformation to prevent physically impossible predictionsLayer thickness expressed as proportions that sum to one the mixture constraintCan I trade-off thickness and layer resin concentration to target 2 performance metrics & minimize a third?Computational Chemistry - Space-Filling Mixture DesignUS Army explosive formulation of “Bread.” Presented last week at JMP Discovery Summit 2017, St. Louis, MO, USA Copyright 2013, SAS Institute Inc. All rights reserved.
REVISIT PLASTICFORMULATION 5 components - names & rangesBinderPlasticizerA MonomerB .150.15 3 additional constraints0.18 A Mon B Mon 0.26A Mon B Mon Plas 0.35 model is 2nd order nonlinear blendingCopyright 2013, SAS Institute Inc. All rights reserved.
POTENTIALLYFITTING HARDNESS OF PLASTIC WITHOUT (TOP) ANDEMBARRASSINGWITH A SQRT TRANSFORMATION (BOTTOM)PREDICTIONSNEGATIVE Value?NEGATIVE Low Limit?POSITIVE Value!ZERO Low Limit!On Transformed Scale (Bottom),Predictions Make Physical SenseCopyright 2013, SAS Institute Inc. All rights reserved.
10-FACTOR 6-MIX,2-CON, 1-CAT, 1-BLKCOMPLEX DOE See step-by-stepPDF for details ofcomplex designconstructionOne inequality constraintBase Filler 0.7Portion of mixture heldconstant at 2%Copyright 2013, SAS Institute Inc. All rights reserved.
7-COMPONENT AND7-CONSTRAINTSMIXTURE DOE See step-by-stepPDF for details ofmixture designconstructionCopyright 2013, SAS Institute Inc. All rights reserved.
THREE-LAYER FILM STRUCTURE,FACTORS AND RANGESFactor choice and rangescome from you and/or yoursubject matter experts!Total Thickness ofThree-Layer Film is24 to 48 micronsLayer A is 25% to 55%of Total ThicknessLayer B is 30% to 70%of Total ThicknessLayer C is 5% to 15%of Total ThicknessLayer A R1Layer B R2 R1Layer C R2 R3Copyright 2013, SAS Institute Inc. All rights reserved.Layer A is 100% Resin 1Layer B is 10% to 90% Resin 2and 90% to 10% Resin 1Layer C is 10% to 90% Resin 2and 90% to 10% Resin 3
WWW.JMP.COM/TECHNICALLY-SPEAKINGGO TO “BOOSTING PERFORMANCE WITHCUSTOM DESIGNED EXPERIMENTS”712Target 700593Target 6000.5%MinimizeAsk JMP to find the best trade-off in performanceamong multiple responses for multiple factorsCopyright 2013, SAS Institute Inc. All rights reserved.
FROM EFFICIENT HOW ARE SPACE-FILLING DESIGNS DIFFERENT FROMM&S TUTORIAL TRADITIONAL RESPONSE-SURFACE DESIGNS?Response-Surface Designfor 3-Variables with 15 Unique TrialsSpace-Filling Designfor 3 Variables with 17 Unique 91X11Rather than emphasizing high leverage trials (“corners”) for a simple polynomialmodel, space-filling designs “spread” their trials more uniformly through thespace to better capture the local complexities of the simulation model.Copyright 2013, SAS Institute Inc. All rights reserved.
US ARMY EXAMPLE SPACE-FILLING MIXTURE DESIGNSCopyright 2013, SAS Institute Inc. All rights reserved.
RESOURCES LINKS TO WEBCASTS, DOWNLOAD PDFS, AND BOOKhttps://www.jmp.com/en tmlhttps://www.jmp.com/en ps://www.jmp.com/en e/prodBK 68410 en.html?storeCode SAS USCopyright 2013, SAS Institute Inc. All rights reserved.
Thanks.Questions or comments?TOM.DONNELLY@JMP.COMCopyright 2010 SAS Institute Inc. All rights reserved.
What makes mixture factors (components) and formulation DOE different? Several Examples Simple three-component designs using Custom DOE platform “Make Designs Fit the Problem –NOT Make Problems Fit the Designs!” Five-component mixture DOE with 3 constraints and respons
Crash Course in Mixture DOE 19 Optimal Design Optimal designs are straightforward to build. First choose components, set their bounds, and add any constraints involving more than 1 component. Crash Course in Mixture DOE 20 Critical in Mixture DOE Constraints like A B 0.3 or B/C 1.3
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Mixture proportion design method of SFRCAC is developed in this paper to obtain concrete with target strength and workability, which can be used in structural members. Four key parameters of mixture proportioning, steel fiber content, water-cement ratio, water content and sand ratio are discussed through the mixture design tests. The formula for
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