Basic Design of Experiments Using the Custom DOE Platform

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Information about Basic Design of Experiments Using the Custom DOE Platform
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Published on April 8, 2014

Author: JMPsoftware

Source: slideshare.net

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These slides provide an overview of the basics of design of experiments. They also describe and give examples of categorical and continuous factors and responses, discrete numeric and mixture variables, and blocking factors. The slides were presented live and in recorded videos as part of the Mastering JMP webcast series. Watch the webcasts at http://www.jmp.com/mastering

Copyright © 2013, SAS Institute Inc. All rights reserved. BASIC DESIGN OF EXPERIMENTS USING CUSTOM DOE PLATFORM Mastering JMP Webcast April 4, 2014 Tom Donnelly, PhD Systems Engineer & Co-insurrectionist JMP Federal Government Team

Copyright © 2013, SAS Institute Inc. All rights reserved. WHY USE DOE? QUICKER ANSWERS, LOWER COSTS, SOLVE BIGGER PROBLEMS • More rapidly answer “what if?” questions • Do sensitivity and trade-space analysis • Optimize across multiple responses • By running efficient subsets of all possible combinations, one can – for the same resources and constraints – solve bigger problems • By running sequences of designs one can be as cost effective as possible & run no more trials than are needed to get a useful answer

Copyright © 2013, SAS Institute Inc. All rights reserved. AGENDA • Example Process Optimization and Trade-Space Analysis • Brief Review of Classic DOE • Real-World Experimental Issues - Making Designs Fit the Problem – NOT Making Problems Fit the Designs! • Types of factors • Bold range setting • Constraints • Custom DOE examples • All continuous factors • Continuous factors with a constraint • Continuous, categorical and blocking factors

Copyright © 2013, SAS Institute Inc. All rights reserved. USE JMP TRADE-OFF AND OPTIMIZATION

Copyright © 2013, SAS Institute Inc. All rights reserved. CLASSIC RESPONSE-SURFACE DOE IN A NUTSHELL Fit requires data from all 3 blocks Can fit data from blocks 1, 2 or 3 Fit requires data from blocks 1 & 2 Lack-of-fitLack-of-fit Block 3Block 1 Block 2 x1 x3 x3x3 x1x1

Copyright © 2013, SAS Institute Inc. All rights reserved. POLYNOMIAL MODELS USED TO CALCULATE SURFACES y = a0 + a1x1 + a2x2 + a3x3 Run this block 1st to: (i) estimate the main effects* (ii) use center point to check for curvature. y = a0 + a1x1 + a2x2 + a3x3 + a12x1x2 + a13x1x3 + a23x2x3 Run this block 2nd to: (i) repeat main effects estimate, (ii) check if process has shifted (iii) add interaction effects to model if needed. y = a0 + a1x1 + a2x2 + a3x3 + a12x1x2 + a13x1x3 + a23x2x3 + a11x1 2 + a22x2 2 + a33x3 2 Run this block 3rd to: (i) repeat main effects estimate, (ii) check if process has shifted (iii) add curvature effects to model if needed. Block 3Block 1 Block 2 x1 x3 x3x3 x1x1

Copyright © 2013, SAS Institute Inc. All rights reserved. NUMBER OF UNIQUE TRIALS FOR 3 RESPONSE-SURFACE DESIGNS AND NUMBER OF QUADRATIC MODEL TERMS VS. NUMBER OF CONTINUOUS FACTORS Unique Trials in Central Composite Design Terms in Quadratic Model Unique Trials in Custom Design with 6 df for Model Error Unique Trials in Box-Behnken Design If generally running 3, 4 or 5-factor fractional-factorial designs… 1. How many interactions are you not investigating? 2. How many more trials needed to fit curvature? 3. Consider two stages: Definitive Screening + Augmentation

Copyright © 2013, SAS Institute Inc. All rights reserved. REAL-WORLD DESIGN ISSUES • 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 with mixed # of levels; 3 chemical agents, 4 decontaminants, 8 coupon materials…) » Mixture/formulation? (Blend different amounts of ingredients and the process performance is dependent on the proportions more than on the amounts) » Blocking? (e.g. “lots” of the same raw materials, multiple “same” machines, samples get processed in “groups” – like “eight in a tray,” run tests over multiple days – i.e. variables for which 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) • 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) • Characterize process or run experiments using computer simulations? (agent-based, discrete event, computational fluid dynamics (CFD)) • Measure response data in vicinity of physical limits? (counts, hardness, resistivity can’t fall below zero, or percentage yield or killed can’t exceed 100%) How many experimenters have any of these issues? Most of these are NOT well treated by classic DOE

Copyright © 2013, SAS Institute Inc. All rights reserved. REAL-WORLD FACTORS

Copyright © 2013, SAS Institute Inc. All rights reserved. CATEGORICAL FACTORS AND RESPONSES • Materials  Steel  Aluminum  Glass  Polycarbonate  CARC (Paint)  Viton  Kapton  Silicone • Agents • Agent 1 • Agent 2 • Agent 3 • Decontaminants • Decon 1 • Decon 2 • Decon 3 • Decon 4 Responses • Pass/Fail • Yes/No • Not Cracked/Cracked • Safe/Caution/Unsafe • Not Corroded/ Moderately Corroded/ Severely Corroded

Copyright © 2013, SAS Institute Inc. All rights reserved. CONTINUOUS FACTORS AND RESPONSES • Factors  Time  Temperature  Amount of Agent/Unit Area  Wind Speed  Humidity • Responses • Evaporation Rate • Absorption • Adsorption • Residual Concentration

Copyright © 2013, SAS Institute Inc. All rights reserved. DISCRETE NUMERIC VARIABLE Example: Number of Teeth on Bicycle Sprockets 16 18 22 24 28 Teeth 16 19 22 25 28 Delta 3 3 3 3 % Change 18.8% 15.8% 13.6% 12.0% Teeth 16 18 22 24 28 Delta 2 4 2 4 % Change 12.5% 22.2% 9.1% 16.7% Teeth 16 18 21 24 28 Delta 2 3 3 4 % Change 12.5% 16.7% 14.3% 16.7% Evenly Spaced Actual Spacing Improved Spacing

Copyright © 2013, SAS Institute Inc. All rights reserved. MIXTURE VARIABLES • Relative proportions of components is more important than actual quantity • Three liquid components - Oil, Water, and Vinegar • 8 oz. in Cruet vs. 4 gal. in Jug 5 oz. “O” 320 oz. 1 oz. “W” 64 oz. 2 oz. “V” 128 oz. • To study these mixture components use ranges that are proportions: O: 0.50 to 0.75 W: 0.10 to 0.20 V: 0.15 to 0.40 • Sum of proportions constrained to equal 1. 100.0% 37.5% 25.0% 0%

Copyright © 2013, SAS Institute Inc. All rights reserved. BLOCKING FACTOR LIKE “DAY” OR “BATCH” • A design run over 5 days that is sensitive to humidity might SHIFT on Thursday  But what if because of the rain the tester from days 1, 2, 3 & 5 didn’t make it to work?  What if that day the power went out briefly? Or, dept. meeting “paused” the work? Or…? • The block variable doesn’t tell you the cause of the effect - just that a shift has been detected among blocks. • Hoping block variable has no effect. If it does then how can we reliably predict other blocks? If significant it probably means we are missing a factor. • The only way to be sure that no “unknown” factor has crept into the experiment, is to test for it - and “blocking” your design is not expensive. • Block variable is a categorical factor having only 1-way effects (no interactions)

Copyright © 2010 SAS Institute Inc. All rights reserved. TOM.DONNELLY@JMP.COM Thanks. Questions or comments?

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