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1 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 1

2 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 2

3 Building Factorial Split Plots Restrict Randomization Split-plot factorial designs: 2-level full and fractional factorials General factorials Optimal (custom) factorials Power for split plots: (2 5-1 fractional factorial) Design-Expert version 9 3

4 Analyzing Factorial Split Plots Factorial split plots analysis: REML variance component estimation GLS parameter estimation Kenward-Roger approximate F-tests Check restricted designs for OLS/GLS equivalence Separate half-normal plots for whole and sub plot factors. Design-Expert version 9 1 a,b,c 4

5 Analyzing Factorial Split Plots REML variance component estimation: Allow negative variance components Use for better estimates of factor effects. Do not allow negative variance components Use for better estimates of variance components. Design-Expert version 9 5

6 New FSPD workshop Workshop Hierarchy Factorial Split-Plot Designs 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 Pharma, Food Science, Life Sciences, or Assay Optimization Workshop descriptions and outlines: Design-Expert version 9 6

7 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 7

8 New Randomized Designs Definitive screening designs: Bradley Jones, Christopher J. Nachtsheim A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects, Technometrics Vol. 43, No. 1, January This fractional three-level DOE choice resolves main effects clear of any two-factor interactions and squared terms Simple sample design: A one-level, one-factor design for a mean only model. Take advantage of powerful features in Design-Expert software for data characterization, diagnostics and graphics for a simple sample of data. Design-Expert version 9 2 a,b 8

9 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 9

10 Journal Feature Easy Export and Documentation Allow the user to send reports (or parts of reports) and graphs to a journal using a mouse right click. Currently supporting Microsoft Word and PowerPoint to collect the reports. Design-Expert version

11 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 11

12 Ignore Factor Columns (Including Blocks) Design-Expert version

13 Constant Ingredients in Mixtures Complete Recipes Entering the same Low and High value for a mixture component defines it as a constant. 83% of the total 100% varies, 17% is fixed. Design-Expert version 9 4a 13

14 New Design Layout Tools Ascending and descending sort of individual columns. Automatically sort by run order after user chooses to randomize existing design. Switch directly between discrete and continuous numeric factor types. Design-Expert version

15 New Design Layout Tools New Built Point Type column (Model, Lack of Fit, Replicate). Allow user to edit Space Point Type column. Design-Expert version 9 4b 15

16 New Point Type Verification Verification runs: Not used for model fitting (ignore in regression) Used to verify the model fit (get diagnostics) Three lack of fit runs are set to be verification runs. Design-Expert version 9 4c 16

17 Verification Points Allow the user to add verification runs. They are not used for fitting the model in the analysis, just like ignored runs. However, unlike ignored runs, they will (if enabled) show up in the diagnostic graphs. They have a [ ] designation in the jump to run list. Display verification points (if enabled) on the diagnostic graphs. (But not displayed on the Influence graphs.) Design-Expert version 9 17

18 Verification Points (page 1 of 3) Drug Stability Characterization FCD Note: Temperature (T) rather than 1/T is plotted on this graph. T a w O 2 points to validate Arrhenius relationship Design-Expert version 9 5 a, b 18

19 Verification Points (page 2 of 3) FCD the Core Design g Design-Expert Software Ln(k-TDP) Color points by value of Ln(k-TDP): Note: On all the diagnostic plots the verification al % Probability Norm Normal Plot of Residuals 1 runs are in-line with the FCD runs; i.e. the model is verified! Residuals Design-Expert version 9 5a 19

20 Ln(k-TPD) Verification Points (page 3 of 3) Arrhenius Model is Valid! a w = 0.05, O 2 = 0.2% a w = 0.35, O 2 = 0.2% R adj = E E E E E-03 A: 1/T Ln(k TPD) R adj = E E E E E-03 A: 1/T Because the Arrhenius model describes the rates as a function of temperature so well, we have confidence to extrapolate degradation rate to room temperature (25 C). Design-Expert version 9 5b 20

21 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 21

22 Graph Columns Correlation Matrix A table with all of the correlation values associated with the Graph Columns tab. Color of the cells is gradient based on correlation value. Clicking on the cell changes the graph in the main window. Click on Customize to see options. Design-Expert version

23 Add LOESS fit line to Graph Columns locally weighted scatter plot smoothing y g p g The subsets of data used for each weighted least squares fit in LOESS are determined by a nearest neighbors algorithm. A user-specified input to the procedure called the "bandwidth determines how much of the data is used to fit each local polynomial. The bandwidth parameter (q) is a number between 0 and 1, with q denoting the portion of the data used. (Right click on the line to change q.) The subset of data used in each weighted least squares fit is comprised of the nq (rounded to the next largest integer) points whose values are closest on the x-axis. Design-Expert Software Correlation: LOESS Bandwidth: Color points by Standard Order Surface (Tack) A:Mw (gm) Design-Expert version

24 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 24

25 Design Evaluation Correlations Factors (page 1 of 2) 6 factor definitive screening design. Full quadratic model. Design-Expert version 9 25

26 Design Evaluation Correlations Coefficients (page 2 of 2) 6 factor definitive screening design. Full quadratic model. Design-Expert version 9 26

27 Design Evaluation and ANOVA X-matrix and Z-matrix (Z only for split plots) Design-Expert version 9 1a 27

28 Design Evaluation One-sided (NEW) and Two-sided FDS Option ( ) p Generally when sizing designs: Use the two-sided confidence interval option on the FDS for functional designs. Use the one-sided tolerance interval option on the FDS for verification (e.g. QbD) designs. Design-Expert version

29 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 29

30 Design Model in Fit Summary Problem: Since design models for combined designs are frequently reduced they do not show up in the Fit Summary and consequently are never selected. Solution: Check the Design Model and, if it is the best, recommend it in the Suggested Models summary at the top of the report. E.g. HPLC combined.dxp The design model was created by choosing Quadratic x Quadratic with a Combined order of Cubic. Suggested models are Linear+Squared x Linear and Quadratic x Linear. In this case, the Design Model is a better choice and now a recommended model. Design-Expert version

31 All Hierarchical Model Selection Added an option to the Model screen to use the branch and bound method of selecting a hierarchical models as described d in: Brusco, Cradit, Steinly (2009) "An Exact Algorithm for Hierarchically Well-Formulated Subsets in Second-Order Polynomial Regression", Techonometrics, 51, Does a pass of Backward selection after All-Hierarchical is done and then fixes hierarchy. h This can be really time consuming for when there are many model terms. Design-Expert version

32 Copy Excel Formula To Paste use Ctrl-V or Paste Special, XML Spreadsheet Design-Expert version

33 Diagnostic Plots Default for diagnostics is Externally Studentized residual.* Changed the Studentized choice in Diagnostics to a three-way choice (using a dropdown list on tool) of: Externally Studentized Internally Studentized Residuals Eliminated the Externally Studentized residual button from influence as it is now redundant. * Geoff Vining (2011). Technical Advice: Residual Plots to Check Assumptions, Quality Engineering, 23: Design-Expert version

34 Jump to run # in Factor Tool The jump to run: Auto-selects the point that was jumped too. This allows the user to easily see which point on the slice is the one they selected. Expand x-axes to include the point jumped to. Default brings you back to the default factor ranges. Design-Expert version

35 R es er ve d. Show Units on axes labels Conversion (%) 88 Al lr ig ht s B : te m p e ra tu re (d e g C ) St at -E as e, I nc Design-Expert version A: time (min.)

36 ve d. Mixture Graph in Reals R es er Evaluation and Model Graphs p Al lr ig ht s Plot three component mixture contour graph using real values with ith 0 to t 1 axis i scaling. li A: A e, I 102 nc. A: A at -E as St B: B C: C 1 B: B C: C R1 14 R The Real Real Contour Contour graph is only available for 3 component mixtures mixtures. Design-Expert version 9 11 a,b 36

37 2 nd Derivative for POE Calculations ( ˆ ) First order approximation ŷ = ( ) f x,...,x 1 k 2 k f f f k Var y 2 i= 1 x i< j x x ( ˆ ) = σ ii + σ ij +σe i i j Second order approximation (process factors only) ŷ = f ( x,...,x ) + σ i k 2 1 f 2 1 k 2 ii 2 i= 1 x k k k 2 k 2 f 2 f f 2 1 f 4 f ii ij 2 ii ii jj e i= 1 x i< j x x 2 i= 1 x i< j x x Var y = σ + 2 σ + σ + σ σ +σ i i j i i j Design-Expert version 9 37

38 POE Options Advanced Preferences Use POE adjustment for intervals and predictions not checked: don t adjust checked: adjust Use 2nd Order POE (process factors only) not checked use 1 st checked use 2 nd Design-Expert version 9 12 a,b 38

39 POE Point Prediction Design-Expert version 9 12b 39

40 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 40

41 Numeric Optimization Added C pk Criteria Design-Expert version

42 Process Capability Refresher C pk statistic pk C pk ( μμ LSL ) Minimum USL, LSL = 3σ LSL Lower Specification Limit μ-lsl 3 σ μ C pk defines the potential capability of the process, with regard to where the process is centered. +3 σ USL-μμ USL Upper Specification Limit Design-Expert version 9 42

43 What s New in Design-Expert version 9 Factorial split plots (Two-Level, Multilevel, Optimal) Definitive Screening and Single Factor designs Journal Feature Design layout Graph Columns Design Evaluation Analysis Optimization Post Analysis Design-Expert version 9 43

44 Created Post-Analysis node Created a new node called Post-Analysis. Moved the Point Prediction node under it. Moved the Confirmation node under it. Created a new node for the Coefficients Table under the Post-Analysis node. Removed the Coefficients Table from the Summary node. Design-Expert version 9 44

45 Confirmation Node User Entry of Confirmation Data Design-Expert version

46 Point Prediction and Confirmation Node Added observed values With the ability to jump to a run in the factors tool, it is useful to be able to see the observed value for that t run in the Point Prediction and Confirmation reports. Design-Expert version

47 Point Prediction Transformation Mean Bias Correction ( ) t( y) The response y is transformed y = -1 Apply the inverse transform (t ) to get the response in the original scale (y) 1 f ( y ˆ) = t ( y ˆ ) The back transformed mean of y' is the median of y. To estimate the mean of y a mean bias correction must be added: ˆ 1 f y = t y + σ 2 yˆ ( ˆ ) 2 ŷy To get the confidence interval use the above formula to transform the estimated median and the end points for the CI on the median. Design-Expert version 9 47 ˆ

48 Transformed Response Bias Correction (page 1 of 2) In the transformed scale the predicted Mean (2.018) and the predicted Median (2.018) are the same. Design-Expert version

49 Transformed Response Bias Correction (page 2 of 2) Due to bias correction the predicted Mean (107.2) and the predicted Median (104.3) are different in the original scale. Design-Expert version

50 Transformed Response Bias Correction Why distribution in transformed scale distribution in original scale Design-Expert version 9 50