Partition Experimental Designs for Sequential Process Steps: Application to Product Development

1. Partition Experimental Designs for Sequential Process Steps: Application to Product Development Leonard Perry, Ph.D., MBB, CSSBB, CQE Associate Professor & ISyE Program Chair Industrial & Systems Engineering (ISyE) University of San Diego

2. Example: Lens Finishing Processes • A company desires to improve their lens finishing process. Experimental runs must be limited due to cost concerns. What type of design do you recommend? Process One: Four Factors Process Two: Six Factors

3. Objective of Partition Designs • To create a experimental design capable of handling a serial process consisting of multiple sequential processes that possess several factors and multiple responses. • Advantages: • Output from first process may be difficult to measure. • Potential interaction between sequential processes • Reduction of experimental runs

4. Design Matrix #1 Design Matrix #2 Responses + = Partition Design

5. Partition Design: Assumptions • Process/Product Knowledge required • Screening Experiment required • Resources limited, minimize runs • Sparsity-of-Effect Principle

6. Perform Screening Experiment for Each Individual Process Construct Partition Design Perform Partition Design Experiment Perform Partition Design Analysis Select Significant Effects for Each Response Build Empirical Model for Each Response Calculate Partition Intercept Select Significant Effects for Intercept Build Final Empirical Model Partition Design: Methodology

7. Review: Experimental Objectives • Product/Process Characterization • Determine which factors are most influential on the observed response. • “Screening” Experiments • Designs: 2k-p Fractional Factorial, Plackett-Burman Designs • Product/Process Improvement • Find the setting for factors that create a desired output or response • Determine model equation to relate factors and observed response • Designs: 2k Factorial, 2k Factorial with Center Points • Product/Process Optimization • Determine an operating or design region in which the important factors lead to the best possible response. (Response Surface) • Designs: Central Composite Designs, Box-Behnken Designs, D-optimal • Product/Process Robustness • Explore settings that minimize the effects of uncontrollable factors • Designs: Taguchi Experiments

8. Example: First-order Partition Design • Two factors significant in each process • Total of k = 4 factors • Potential Interaction between processes • Partition Design • N = 5 runs (N = k - 1) (Saturated Design)

9. Step 1: Perform Screening Experiment • Process 1: • Significant Factors: • Factor A • Factor B • Process 2: • Significant Factors: • Factor C • Factor D

10. Step 2: Construct Partition Design • Partition Design: Design Criteria • First-order models • Orthogonal • D-optimal • Minimize Alias Confounding • Second-order models • D-efficiency • G-efficiency • Minimize Alias Confounding

11. Step 2: Construct Partition Design • First-order Design (Res III or Saturated) • Orthogonal • D-optimality • Minimize Alias Confounding

12. Step 2: Construct Partition Design Term Aliases Model A-A BD CD ABC Model B-B AB BC BD ABC ABD BCD Error C-C AB AD BC BD ABC ABD BCD Error D-D AB AC BCD

13. Step 3: Perform Partition Design Experiment • Planning is key • Requires increased coordination between process steps • Identification of Outputs and Inputs

14. Step 4: Perform Partition Design Analysis For Each Response: • Select Significant Effects • Build Empirical Model • Calculate Partition Intercept Response • Select Significant Effects for Intercept Response

15. Step 4a: Select Significant Effects

16. Step 4a: Select Significant Effects

17. Step 4b: Build Empirical Model

18. Step 4c:Calculate Partition Intercept Response Run 1 Int1i = - 8.85A - 16.47B + y1i Int11 = - 8.85(1) - 16.47(1) + 34.4 Int11 = 9.101 Calculations Int1i = - 8.85A - 16.47B + y1i for i= 1 to N

19. Step 4: Partition Analysis • Repeat for Second Partition • Select Significant Effects • Build Empirical Model • Calculate Partition Intercept Response

20. Step 4d:Select Significant Effects for Intercept

21. Step 5:Build Final Empirical Model

22. Controllable factors k x x x 2 1 Controllable factors . . . k x x x 2 1 . . . Manufacturing Outputs, y Process #1 Inputs Manufacturing Outputs, y Process #2 . . . Inputs z z z 1 2 r . . . Uncontrollable factors z z z 1 2 r Uncontrollable factors Case Study: Biogen IDEC • Q8 Design Space • Link input parameters with quality attributes over broad range • Traditional Design of Experiments (DOE) • Systematic approach to study effects of multiple factors on process performance • Limitation: not applied to multiple sequential process steps; does not account for the effects of upstream process factors on downstream process outputs

23. Case Study: Biogen IDEC Partition Design: Experimental • Resolution IV: 1/16 fractional factorial for whole design • Each partition: full factorial • Harvest pH included in Protein A partition • Each column: 16 expts + 4 center points = 20 expts Controllable factors Controllable factors Controllable factors pH 4.5 pool pH 5.75 pool pH 7 pool x x x x x x x x x 1 2 k 1 2 k 2 1 k 20 CEX eluate pools 20 Protein-A eluate pools . . . . . . . . . Harvest Protein-A CIEX . . . . . . . . . z z z z z z z z z 1 2 r 1 2 r 2 1 r Uncontrollable factors Uncontrollable factors Uncontrollable factors

24. Protein-A Chromatography Step Cation Chromatography Step Elution Load Elution Mab Eluate Load Wash NaCl Elution Harvest Wash I Experiment Capacity velocity from Capacity volume Conc. pH pH Conc. (%) (cm/hr) Experiment # (%) (CV) (mM) (mM) 1 5.75 75 2100 262.5 1 70 3 155 5.5 2 4.5 120 0 75 2 110 2 185 6 3 30 4 185 6 3 7 30 0 75 4 110 2 185 5 4 7 30 0 450 5 30 2 125 5 5 4.5 30 0 75 6 110 4 185 5 6 4.5 30 4200 75 7 110 2 125 6 7 7 30 4200 75 8 30 2 185 6 8 4.5 30 4200 450 9 30 2 185 5 9 7 120 4200 75 10 70 3 155 5.5 10 5.75 75 2100 262.5 11 70 3 155 5.5 11 5.75 75 2100 262.5 12 110 4 125 6 12 4.5 30 0 450 13 110 4 125 5 13 7 120 0 75 14 30 4 185 5 14 4.5 120 0 450 15 30 2 125 6 15 7 120 0 450 16 30 4 125 6 16 4.5 120 4200 75 17 30 4 125 5 17 7 30 4200 450 18 110 2 125 5 18 4.5 120 4200 450 19 110 4 185 6 19 7 120 4200 450 20 70 3 155 5.5 20 5.75 75 2100 262.5 Partition Design: Designs

25. CIEX Step HCP ANOVA Comparison: Main Effects Partition Model Results Traditional Model Results • Partition model identified same significant main factors and their relative rank in significance

26. CIEX Step HCP ANOVA Comparison: Interactions Partition Model Results Traditional Model Results • Partition model able to identify interactions between process steps

27. Summary of Partition Designs Experimental design capable of handling a serial process Sequential process steps that possess several factors and multiple responses Potential Advantages Links process steps together: identify upstream operation effects and interactions to downstream processes. Better understanding of the overall process Potentially less experiments No manipulation of uncontrollable parameters necessary Controllable factors Controllable factors Controllable factors x x x x x x x x x 1 2 k 1 2 k 1 2 k . . . . . . . . . Outputs, y Outputs, y Outputs, y Manufacturing Manufacturing Manufacturing Process #2 Process #3 Process #1 Inputs Inputs Inputs . . . . . . . . . z z z z z z z z z 1 2 r 1 2 r 1 2 r Uncontrollable factors Uncontrollable factors Uncontrollable factors

28. References • D. E. Coleman and D. C. Montgomery (1993), ‘Systematic Approach to Planning for a Designed Industrial Experiment’, Technometrics, 35, 1-27. • Lin, D.J.K. (1993). "Another Look at First-Order Saturated Designs: The p-efficient Designs," Technometrics, 35: (3), p284-292. • Montgomery, D.C., Borror, C.M. and Stanley, J.D., (1997). “Some Cautions in the Use of Plackett-Burman Designs,” Quality Engineering, 10, 371-381. • Box, G. E. P. and Draper, N. R. (1987) Empirical Model Building and Response Surfaces, John Wiley, New York, NY • Box, G. E. P. and Wilson, K. B. (1951), “On the Experimental Attainment of Optimal Conditions,” Journal of the Royal Statistical Society, 13, 1-45. • Hartley, H. O. (1959), “Smallest composite design for quadratic response surfaces,” Biometrics 15, 611-624. • Khuri, A. I. (1988), “A Measure of Rotatability for Response Surface Designs,” Technometrics, 30, 95-104. • Perry, L. A., Montgomery, and D. C, Fowler, J. W., " Partition Experimental Designs for Sequential Processes: Part I - First Order Models ", Quality and Reliability Engineering International, 18,1.