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1 A Flexible Strategy for More Effective Experimentation Taking Designs Apart and Putting Them Together Again Communication issues: To prevent audio disruptions, we must mute all for these worldwide webinars. Also, to avoid interrupting the presentation, the live question option will not be enabled. However, we do want to hear from you! So please follow up with via to which will be promptly answered by me or one of my fellow Stat-Ease Consultants. Shari By Shari L Kraber, PE Stat-Ease, Inc., Minneapolis, MN shari@statease.com Slides posted at Flexible DOE Strategy 1

2 Objective for this Webinar Demonstrate a few ways you can do DOE s differently. Build up from a one factor at a time study, or augment designs that don t provide all the information you needed. Please press the raise hand if you are with me. Raise-Hand button Flexible DOE Strategy 2

3 A Flexible DOE Strategy Foldover method for factorials Semifold method Building a CCD from OFAT Optimal augmentation for response surface designs Flexible DOE Strategy 3

4 What is a foldover? A B C Add the opposite runs the other half of the design. A B C This will change a Resolution III design into a Resolution IV design (or higher). But watch out for designs that are already Res IV Flexible DOE Strategy 4

5 7 factor in 8 run (Res III) design The 7 factor in 8 run design is a popular choice. Flexible DOE Strategy 5

6 Validation (Ruggedness) Testing Moisture Determination Here is the half-normal plot for this set of data: Design-Expert Software Water Shapiro-Wilk test W-value = p-value = A: Reagent B: Reac time C: n-heptane D: Dis time E: Dis rate F: Aniline G: Hydration Positive Effects Negative Effects Probability Ha lf-normal % Half-Normal Plot A Effect Flexible DOE Strategy 6

7 Use design evaluation to see aliases: Factorial Effects Aliases [Est. Terms] Aliased Terms [Intercept] = Intercept [A] = A + BD + CE + FG [B] = B + AD + CF + EG [C] = C + AE + BF + DG [D] = D+AB+CG+EF + + [E] = E + AC + BG + DF [F] = F + AG + BC + DE [G] = G + AF + BE + CD Hint: On Design Evaluation ignore 3FI: Validation Testing Moisture Determination Flexible DOE Strategy 7

8 Validation Testing Moisture Determination We must augment the original resolution III design to separate factor A from the 2FIs it is aliased with. [A] = A + BD + CE + FG Complete foldover: Create a new block of runs with the factor levels at the opposite settings of the original design. Change all signs on all the original runs. Resolution III designs: Separates the main effects from the two factor interactions, producing a resolution IV design. Flexible DOE Strategy 8

9 Foldover the design: 1. Click on the Design node. 2. From the Design Tools menu choose Augment Design Augment. gment 3. For augmenting method choose Fold over and click OK. 4. Use the default of folding on all factors and click OK. Exploring Aliased Terms Complete Foldover 5. To assure new runs will clear up confusion from aliases, evaluate the design prior to performing additional runs. Flexible DOE Strategy 9

10 Exploring Aliased Terms Complete Foldover Std Factor 1 Factor 2 Factor 3 Factor 4 Factor 5 Factor 6 Factor 7 1 Block 1 used ca 2 2 Block 1 new ca 5 3 Block 1 used ca 5 4 Block 1 new ca 2 5 Block 1 used ca 5 6 Block 1 new ca 2 7 Block 1 used ca 2 8 Block 1 new ca 5 9 Block 2 new ca 5 10 Block 2 used ca 2 11 Block 2 new ca 2 12 Block 2 used ca 5 13 Block 2 new ca 2 14 Block 2 used ca 5 15 Block 2 new ca 5 16 Block 2 used ca 2 Flexible DOE Strategy 10

11 extra material Complete Foldover The defining relation for the original design (block 1) is: I = ABD = ACE = BCDE = BCF = ACDF = ABEF = DEF = ABCG = CDG = BEG = ADEG = AFG = BDFG = CEFG = ABCDEFG The levels of each factor in the foldover (block 2) are the opposite of those in the original design. Where a factor was +1 in the first block, it is 1 inthe second. The defining relation for block 2 is: I = ABD = ACE = BCDE = BCF = ACDF = ABEF = DEF = ABCG = CDG = BEG = ADEG = AFG = BDFG = CEFG = ABCDEFG Combining the two blocks: 2I = = = 2BCDE = = 2ACDF = 2ABEF = = 2ABCG = = = 2ADEG = = 2BDFG = 2CEFG = I = BCDE = ACDF = ABEF = ABCG = ADEG = BDFG = CEFG After a complete foldover all odd length words are eliminated! Flexible DOE Strategy 11

12 Exploring Aliased Terms Complete Foldover Water used One Factor A: Reagent new After the foldover the chemist identifies an additive in the new adhesive causing an azeotrope to occur while distilling the water from the used reagent. [A] = A + BCG + BEF + CDF + DEG Flexible DOE Strategy 12

13 Coating Thickness Screening A spin coater is used to apply a photo resist to a silicon wafer. Six factors are thought likely to affect coating thickness: Spin speed 0-8,000 RPM Programmable acceleration Volume of resist Programmable spin time Vendor supplying resist Exhaust (cover on or off) Flexible DOE Strategy 13

14 Coating Thickness Screening (page 1 of 3) Use Design-Expert to design your experiments. Use the fractional factorial, i.e., 6 factors in 16 runs. The response is: Flexible DOE Strategy 14

15 Use the design Evaluation node to examine the aliases. Evaluation; Order: 3FI, Ignore: 4FI Coating Thickness Screening Factorial Effects Aliases [Est. Terms] Aliased Terms [Intercept] = Intercept [A] = A + BCE + DEF [B] = B + ACE + CDF [C] = C + ABE + BDF [D] = D + AEF + BCF [E] = E + ABC + ADF [F] = F + ADE + BCD [AB] = AB + CE [AC] = AC + BE [AD] = AD + EF [AE] = AE + BC + DF [AF] = AF + DE [BD] = BD + CF [BF] = BF + CD [ABD] = ABD + ACF + BEF + CDE [ABF] = ABF + ACD + BDE + CEF Flexible DOE Strategy 15

16 Exploring Aliased Interactions Coating Thickness Design-Expert Software Thickness Shapiro-Wilk test W-value = p-value = A: Spin speed B: Acceleration C: Volume D: Spin time E: Resist F: Exhaust Positive Effects Negative Effects Normal % Prob bability Ha lf Half-Normal Plot C B E AB A Effect Flexible DOE Strategy 16

17 Exploring Aliased Interactions Coating Thickness: AB interaction Th ickness B+ B- Interaction B: Acceleration Thickness = *A *B *C *E *A*B A: Spin speed Flexible DOE Strategy 17

18 Exploring Aliased Interactions Coating Thickness Use a right click to choose among the aliased terms. Replace AB with ithce Flexible DOE Strategy 18

19 Exploring Aliased Interactions Coating Thickness: CE interaction Th ickness E- E+ Interaction E: Resi st Thickness = *A *B *C *E *C*E This is the only part of the equation that changes. All coefficients stay the same! C: Volume Flexible DOE Strategy 19

20 Exploring Aliased Interactions Coating Thickness: CE interaction What factor levels ( 1/+1) minimize thickness? 1. Using the model with AB: A = -1 B = -1 C = -1 E = Using the model with CE: A = -1 B = +1 C = +1 E = +1 How do you set the process if you don t know which model is correct? Flexible DOE Strategy 20

21 Exploring Aliased Interactions Coating Thickness Th ickness B+ B- Interaction B: Acceleration A: Spin speed What is significant: AB, CE or both? Th h ickness E- E+ Interaction E: Resist C: Volume The answer requires folding on a single factor to free that factor and all the 2FIs involving that factor from aliases with main effects and 2FIs. Thus, folding our design on factor A separates AB from CE. Flexible DOE Strategy 21

22 Fold over the design: 1. Click on the Design node. Exploring Aliased Interactions Coating Thickness: Single Factor Foldover 2. From the Design Tools menu choose Augment Design Augment. 3. For augmenting method choose Fold over and click OK. 4. For single factor foldover select only factor A and click OK. 5. To assure new runs will clear up confusion from aliases, evaluate the design prior to performing additional runs. Flexible DOE Strategy 22

23 Exploring Aliased Interactions Coating Thickness: Single Factor Foldover The defining relation for the original design (block 1) is: I = ABCE = ADEF = BCDF extra material The levels of factor A in the foldover (block 2) are the opposite of those in the original design. Where it was +1 in the first block, it is 1 in the second. The defining relation for block 2 is: I = ABCE = ADEF = BCDF Combining the two blocks: 2I = = = 2BCDF or I = BCDF To determine the defining relation after a single factor foldover, drop all words containing that factor. Flexible DOE Strategy 23

24 Exploring Aliased Interactions Coating Thickness: Complete Foldover The defining relation for the original design (block 1) is: I = ABCE = ADEF = BCDF extra material The levels all factors in the foldover (block 2) are the opposite of those in the original design. Where it was +1 in the first block, it is 1 in the second. The defining relation for block 2 is: I = ABCE = ADEF = BCDF Combining the two blocks: 2I = 2ABCE = 2ADEF = 2BCDF or I = ABCE = ADEF = BCDF A complete foldover replicated the existing runs and did not improve the resolution. Use the single factor foldover. Flexible DOE Strategy 24

25 Exploring Aliased Interactions Coating Thickness: Single Factor Foldover Fractional Factorial Folded on factor A [Intercept] = Intercept [Intercept] = Intercept + BCDF [A] = A + BCE + DEF [Block 1] = Block 1 + ABCE + ADEF [B] = B + ACE + CDF [Block 2] = Block 2 ABCE ADEF [C] = C + ABE + BDF [A] = A [D] = D + AEF + BCF [B] = B + CDF [E] = E + ABC + ADF [C] = C + BDF [F] = F + ADE + BCD [D] = D + BCF [AB] = AB + CE [E] = E [AC] = AC + BE [F] = F + BCD [AD] = AD + EF [AB] = AB + ACDF [AE] = AE + BC + DF [AC] = AC + ABDF [AF] = AF + DE [AD] = AD + ABCF [BD] = BD + CF [AE] = AE [BF] = BF + CD [AF] = AF + ABCD [ABD] = ABD + ACF + BEF + CDE [BC] = BC + DF [ABF] = ABF + ACD + BDE + CEF [BD] = BD + CF [BE] = BE + CDEF [BF] = BF + CD [CE] = CE + BDEF [DE] = DE + BCEF [EF] = EF + BCDE Also note that many more 3 factor and higher [ABC] = ABC + ADF [ABD] = ABD + ACF interactions can be estimated. This will lead us [ABE] = ABE [ABF] = ABF + ACD [ACE] = ACE to semi-folding later in this webinar. [ADE] = ADE [AEF] = AEF [BCE] = BCE + DEF [BDE] = BDE + CEF [BEF] = BEF + CDE [ABDE] = ABDE + ACEF Flexible DOE Strategy [ABEF] = ABEF + ACDE 25 Go to design Evaluation and look at the aliases for the folded design. Now all the 2FIs involving A can be estimated.

26 A Flexible DOE Strategy Foldover method for factorials Semifold method Building a CCD from OFAT Optimal augmentation for response surface designs Flexible DOE Strategy 26

27 Exploring Aliased Interactions Semifold* When folding a 2 k-p resolution IV design on a single factor: The number of additional 2FIs that can be estimated beyond the original design is usually less than half the number of runs of the foldover fraction. If the goals are to both estimate additional 2FIs and increase power, then foldover is a good choice. If the goal is primarily to estimate additional 2FIs, then foldover is not very efficient. A semifold of a resolution IV design generally allows estimation of as many new 2FIs as the foldover. Flexible DOE Strategy 27

28 Exploring Aliased Interactions Coating Thickness: Semifold Semifold subsets the foldover fraction into two groups and only one of the groups is run. The number of new runs are half those of the original design thus achieving a substantial savings compared to foldover! Pick a single factor for the foldover; use factor A. Pick a factor not involved in the interactions we want to separate to subset on. Since F-Exhaust isn t a significant effect we ll subset using F. We would rather have the cover on than off, so keep the on and toss the off. Flexible DOE Strategy 28

29 1. From the Design Tools menu choose Augment Design, Augment. 2. For augmenting method choose Semifold and click OK. 3. Chose factor A as the factor to fold on. 4. Chose the plus level (cover on) of factor F to retain runs; choose F+. 5. To assure new runs will clear up confusion from aliases, evaluate the design prior to performing additional runs. Exploring Aliased Interactions Coating Thickness: Semifold Flexible DOE Strategy 29

30 Exploring Aliased Interactions Coating Thickness: Semifold Go to design Evaluation and look at the aliases for the semifold design: Aliases for main effects and 2FIs are similar. The full fold estimates ten 3FIs and two 4FIs while the semifold can only estimate four 3FIs. In other words the eight extra runs in the full fold get us six 3FIs and two 4FIs. The full fold also has higher power. Semifold: [Intercept] = Intercept - ADE [Block 1] = Block 1 + ADE [Block 2] = Block 2 - ADE [A] = A + BCE + DEF [B] = B + CDF [C] = C + BDF [D] = D + AEF + BCF [E] = E + ABC + ADF [F] = F + ADE + BCD [AB] = AB - BDE - CEF [AC] = AC - BEF - CDE [AD]=AD+ABC+ADF ABC + ADF [AE] = AE + AEF [AF] = AF -BCE-DEF [BC] = BC + DF - AEF [BD] = BD + CF [BE] = BE + BEF + CDE [BF] = BF + CD [CE] = CE + BDE + CEF [DE] = DE + BCE + DEF [EF] = EF - ABC - ADF Full fold: [Intercept] = Intercept + BCDF [Block 1] = Block 1 + ABCE + ADEF [Block 2] = Block 2 - ABCE ADEF [A] = A [B] = B + CDF [C] = C + BDF [D] = D + BCF [E] = E [F] = F + BCD [AB] = AB + ACDF [AC] = AC + ABDF [AD] = AD + ABCF [AE] = AE [AF] = AF + ABCD [BC] = BC + DF [BD] = BD + CF [BE] = BE + CDEF [BF] = BF + CD [CE] = CE + BDEF [DE] = DE + BCEF [EF] = EF + BCDE Flexible DOE Strategy 30

31 Foldover Options 1. Complete foldover: Changing all signs on all the original runs. Resolution III designs: Separates main effects from two-factor interactions, producing a resolution IV design. Resolution IV designs: May produce a replicate of the original fraction, in which case it doesn t improve resolution. 2. Single factor foldover: Changing the signs on only one factor in the original runs. Resolution III and IV designs: The foldover factor and all of its twofactor interactions will be clear of any other main effect or twofactor interaction. 3. Semifold: for a resolution IV design, generally allows estimation of as many new 2FIs as a foldover. 4. Choose a high resolution design to begin with. Flexible DOE Strategy 31

32 Coating Thickness MR-5 Design What would it have cost us to design for interactions to begin with? Spin speed 0-8,000 RPM Programmable acceleration Volume of resist Programmable spin time Vendor supplying resist Exhaust (cover on or off) Try the Minimum-Run Characterize Designs! Flexible DOE Strategy 32

33 Design Resolution Runs screening IV 16 Foldover IV 32 Semifold IV fraction VI 32 MR-5 V 22 Coating Thickness Summary At least consider a resolution V fraction before deciding to screen for main effects using a resolution IV design. Flexible DOE Strategy 33

34 A Flexible DOE Strategy Foldover method for factorials Semifold method Building a CCD from OFAT Optimal augmentation for response surface designs Flexible DOE Strategy 34

35 One Factor At A Time (OFAT) What if your standard condition is okay but you want to see if there is a more optimal condition nearby? Test what happens if you vary the factors higher or lower than the standard condition. Factor B Factor A Flexible DOE Strategy 35

36 OFAT converted to a CCD Now add to that data the corner points of the square, and you will complete the Face-Centered Central Composite design! (This allows you to simply expand from existing data!!!) Factor B Factor A An example Flexible DOE Strategy 36

37 Fluid-Bed Coating FCD Exercise The Process: An air stream separates particles so they can be spray-coated while suspended, thus preventing agglomeration from occurring. The coated particles remain fluidized d just enough to allow them to continue moving towards the bottom of the bowl. When the particles reach the bottom they are drawn back into the high velocity air stream and the cycle is repeated. This process continues until the desired level of coating has been achieved. Encapsulating Solid Particles Flexible DOE Strategy 37

38 Problem: Agglomeration is too high. Responses: Factors: Fluid-Bed Coating Encapsulating Solid Particles 1. Particle size growth, % (minimize, zero is ideal) 2. Throughput, h Load/(Coat time), kg/hr (maximize) i A. Nozzle delivery rate: 300 to 500 g/min B. Atomizing air pressure: 40 to 80 psi C. Fluidizing air: 600 to 800 scfm D. Load: 23 to 32 kg Flexible DOE Strategy 38

39 Fluid-Bed Coating Optimize via a FCD (page 1 of 2) The factor ranges define both the region of interest and operability so use a face-centered centered central composite design. Build the FCD by choosing from the Response Surface tab the Central Composite design for 4 factors. Enter these as follows: Do your alpha and +alpha match levels show above? If not, then what did you forget to do? (Hint: Click Options.) ) Flexible DOE Strategy 39

40 Run the axial points first No analysis, just visual inspection any areas with lower growth?? Yes, so proceed to fill out with hfactorial points Flexible DOE Strategy 40

41 Add factorial (corner) points Flexible DOE Strategy 41

42 Complete Response Surface Analysis The best conditions (minimal Growth) are shown to be at intermediate values of all the factors. The AD interaction could not have been understood with just the OFAT design. Design-Expert Software Factor Coding: Actual Growth (%) X1 = A: Nozzle rate X2 = D: Load Actual Factors B: Atomizing press = C: Fluidizing air = D: Load (kg g) Growth (%) A: Nozzle rate (g/min) Flexible DOE Strategy 42

43 OFAT to CCD Summary Stage 1 - OFAT Start with the axial points (may use existing data) Inspect the results for evidence of potentially good results (no statistical analysis here) Stage 2 - CCD If potential exists expand by adding the factorial (corner) points Complete the RSM analysis and optimize!! Flexible DOE Strategy 43

44 A Flexible DOE Strategy Foldover method for factorials Semifold method Building a CCD from OFAT Optimal augmentation for response surface designs Flexible DOE Strategy 44

45 Problem: Design Augmentation Vinyl Solubility Case To lengthen the life of concrete, a vinyl compound must be dissolved in water prior to the mixing. Your task is to run a central composite design (use rotatable alpha, i.e ) to maximize i the rate of dissolution (solubility) as a function of these 2 factors: A. Temperature (25 to 40 deg C.) B. Stirring rate (50 to 150 rpm) Response: As indicated by the heading for this slide, this is only the beginning! Flexible DOE Strategy 45

46 Here s the data: Design Augmentation Vinyl Solubility Case Flexible DOE Strategy 46

47 Fit Summary: Some problems with the fit?? Summary (detailed tables shown below) Design Augmentation Vinyl Solubility Case Sequential Lack of Fit Adjusted Predicted Source p-value p-value R-Squared R-Squared Linear FI Quadratic Suggested Cubic Aliased Flexible DOE Strategy 47

48 Design Augmentation Vinyl Solubility Case Maybe a higher order model could do a better job of fitting the corners Design-Expert Software Factor Coding: Actual Solubility (gm / 500 ml) Design points above predicted value Design points below predicted value X1 = A: Temperature X2 = B: Stirring 0 ml) So olubility (gm / B: Stirring (rpm) A: Temperature (deg C) Flexible DOE Strategy 48

49 Design Augmentation How to Repair an Inadequate Design Standard RSM designs (CCD, Box-Behnken) cannot fit all the terms in a cubic model. If analysis indicates you need to go to this thirdorder polynomial level, but some or all of the terms remain aliased, the design must be augmented with a second block of runs specifically chosen for this purpose. You need at least one additional run for each aliased coefficient plus one run to make the block correction. (Design-Expert defaults to two runs per coefficient.) It will be most instructive to work on the vinyl design and see what happens. Let s do it! Flexible DOE Strategy 49

50 Design Augmentation Vinyl Solubility: Aliases for Cubic Model First, let s do a design Evaluation with the Order set to Cubic and view the aliases shown in the Results. [A] = A + 2*A 3 [B] = B + 2*B 3 [AB] = AB [A 2 ] = A 2 [B 2 ] = B 2 [A 2 B] = A 2 B B 3 [AB 2 ] = AB 2 A 3 Note that ttwo cubic terms (A 3 &B 3 ) and a block kt term (i (since the additional runs will be in a new block), need to be resolved; so at least three more runs will be needed. Flexible DOE Strategy 50

51 Design Augmentation Vinyl Solubility To augment the central composite design from the design layout screen, go to Design Tools, Augment Design and Augment. Flexible DOE Strategy 51

52 Design Augmentation Vinyl Solubility Click on [Edit model] and change the Order to Cubic. OK the change. Note that the program recommends 6, not 3, additional runs (double the minimum). Flexible DOE Strategy 52

53 Runs added from augmentation: Design Augmentation Vinyl Solubility: Final Analysis These runs, combined with the original runs, can now fit a cubic model. Flexible DOE Strategy 53

54 Vinyl Case (Design Augmentation). Final Results: Contour & 3D Plots e, In c Cubic model works! Set temp at 40º 40º C. as 60 Solubility B : S tirrin g St S o luu b ility 54 at -E B: Stirring A: Temperature Flexible DOE Strategy A Temperature A: T t 54

55 CCD to Optimal Cubic Summary Run the standard central composite design, fitting up to a quadratic polynomial If none of the lower-level polynomials fits well, and there is evidence that a cubic model may fit, then augment optimally and complete the additional runs. Look for: Significant p-value Insignificant lack of fit Higher R-squared values Flexible DOE Strategy 55

56 Objective for this Webinar Checking in (last time!) Demonstrate a few ways you can do DOE s differently. Build up from a one factor at a time study, or augment designs that don t provide all the information you needed.* *We want to hear from you! Take a moment now to note questions for follow up via to stathelp@statease.com. Flexible DOE Strategy 56

57 Now in 2 nd edition*! Web-Based Launch Pad (Chapters 1-3) References DOE, RSM and Mixture Design Formulation SIMPLIFIED Finding the Sweet Spot via Design and Analysis of Experiments with Mixtures A: Apple B: Cinnamon C: Lemon A Primer on Mixture Design: What s In It for Formulators? pubs/mixprimer.pdf p p Flexible DOE Strategy * Productivity Press (CRC, Taylor & Francis) New York,

58 Educational Communications on DOE Bimonthly DOE FAQ Alert Subscribe at: Triannual Stat-Teaser newsletter Link to digital posts provided via DOE FAQ Alert Sign up to get them directly by from homepage StatsMadeEasy Blog at Enjoy periodic posts with A wry look at all things statistical and/or scientific with an engineering perspective. Flexible DOE Strategy 58

59 How to get help Search publications posted at In Stat-Ease software press for Screen Tips, view reports in annotated mode, look for context-sensitive Help (right-click) or search the main Help system. for answers from Stat-Ease s staff of statistical consultants. Call and ask for statistical help. Flexible DOE Strategy 59

60 Factorial Split-Plot Designs Shari Kraber, Workshop Manager & Master Statistician Stat-Ease Training: Computer-Intensive t Statistical ti ti lworkshops Experiment Design Made Easy Response Surface Methods for Process Optimization Robust Design and Tolerance Analysis PreDOE Web-Based (optional) Mixture Design for Optimal Formulations Advanced Formulation: Combining Mixture and Process Variables Basic Statistics for Design of Experiments Designed Experiments for Food Science or Pharma or Life Sciences or Assay Optimization Flexible DOE Strategy 60

61 Statistics Made Easy Best of luck for your experimenting! Thanks for listening! -- Shari Shari L. Kraber, PE Stat-Ease, Inc. Presentation slides and (eventually) a recording posted at For alert on new webinars, subscribe to DOE FAQ Alert at Flexible DOE Strategy 61