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 1

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? 2 Process One: Four Factors Process Two: Six Factors

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 3

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

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

Partition Design: Methodology 6 1. Perform Screening Experiment for Each Individual Process 2. Construct Partition Design 3. Perform Partition Design Experiment 4. Perform Partition Design Analysis a) Select Significant Effects for Each Response b) Build Empirical Model for Each Response c) Calculate Partition Intercept d) Select Significant Effects for Intercept 5. Build Final Empirical Model

Review: Experimental Objectives Product/Process Characterization  Determine which factors are most influential on the observed response.  “Screening” Experiments  Designs: 2 k-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: 2 k Factorial, 2 k 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 7

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) 8

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

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 10

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

Step 2: Construct Partition Design 12 TermAliases ModelA-ABD CD ABC ModelB-BAB BC BD ABC ABD BCD ErrorC-CAB AD BC BD ABC ABD BCD ErrorD-DAB AC BCD

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

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

Step 4a: Select Significant Effects 15

Step 4a: Select Significant Effects 16

Step 4b: Build Empirical Model 17

Step 4c: Calculate Partition Intercept Response 18 Calculations Int1 i = A B + y1 i for i= 1 to N Run 1 Int1 i = A B + y1 i Int1 1 = (1) (1) Int1 1 = 9.101

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

Step 4d: Select Significant Effects for Intercept 20

Step 5: Build Final Empirical Model 21

Manufacturing Process #1 Controllable factors Uncontrollable factors Inputs Outputs, y x 1 x 2 x k z 1 z 2 z r... 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 Case Study: Biogen IDEC Manufacturing Process #2 Controllable factors Uncontrollable factors Inputs Outputs, y x 1 x 2 x k z 1 z 2 z r... 22

Protein-A Controllable factors Uncontrollable factors x 1 x 2 x k z 1 z 2 z r... CIEX Controllable factors Uncontrollable factors x 1 x 2 x k z 1 z 2 z r... pH 4.5 pool pH 5.75 pool pH 7 pool 20 Protein-A eluate pools 20 CEX eluate pools Harvest Controllable factors Uncontrollable factors x 1 x 2 x k z 1 z 2 z r... 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 23

Partition Design: Designs 24

25 Input Parameter % of Total Sum of Squares Load HCP [f(Harvest pH, ProA Wash I)] 83.3 CIEX Elution pH 6.6 Load HCP Load HCP * Elution pH1.6 CIEX Elution [NaCl] 1.1 CIEX Elution pH CIEX Elution [NaCl] * CIEX Elution pH0.5 Load HCP * CIEX Elution [NaCl]0.2 CIEX Load Capacity 0.1 R2R Adjusted R Predicted R Input Parameter % of Total Sum of Squares Harvest pH 32.6 Pro A Wash I Conc Harvest pH * Pro A Wash I 15.6 CIEX Elution pH 10.1 Harvest pH * CIEX Elution pH8.8 Pro A Wash I. * CIEX Elution pH4.6 CIEX Load Capacity 3.9 Pro A Wash I. Conc. * CIEX Elution NaCl1.8 CIEX Elution [NaCl] 1.5 Harvest pH * CIEX Elution [NaCl]1.2 CIEX Elution [NaCl] * CIEX Elution pH 0.2 R2R Adjusted R Predicted R Traditional Model Results Partition Model Results CIEX Step HCP ANOVA Comparison: Main Effects Partition model identified same significant main factors and their relative rank in significance

26 Input Parameter % Sum of Squares Load HCP [f(A,C)] 83.3 CIEX Elution pH 6.6 Load HCP Load HCP * CIEX Elution pH1.6 Elution [NaCl] 1.1 Elution pH Elution [NaCl] * CIEX Elution pH0.5 Load HCP * CIEX Elution [NaCl]0.2 SPXL Load Capacity (mg/ml) 0.1 Input Parameter % of Total Sum of Squares Harvest pH 32.6 Pro A Wash I Conc Harvest pH * Pro A Wash I conc15.6 CIEX Elution pH 10.1 Harvest pH * CIEX Elution pH8.8 Pro A Wash I. Conc.* CIEX Elution pH4.6 CIEX Load Capacity 3.9 ProA Wash 1. * CIEX Elution NaCl1.8 Elution [NaCl] 1.5 Harvest pH * CIEX Elution [NaCl]1.2 CIEX Elution [NaCl] * CIEX Elution pH0.2 Traditional Model Results Partition Model Results Partition model able to identify interactions between process steps CIEX Step HCP ANOVA Comparison: Interactions

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 Manufacturing Process #1 Controllable factors Uncontrollable factors Inputs Outputs, y x 1 x 2 x k z 1 z 2 z r... Manufacturing Process #2 Controllable factors Uncontrollable factors Inputs Outputs, y x 1 x 2 x k z 1 z 2 z r... Manufacturing Process #3 Controllable factors Uncontrollable factors Inputs Outputs, y x 1 x 2 x k z 1 z 2 z r...

References D. E. Coleman and D. C. Montgomery (1993), ‘Systematic Approach to Planning for a Designed Industrial Experiment’, Technometrics, 35, Lin, D.J.K. (1993). "Another Look at First-Order Saturated Designs: The p- efficient Designs," Technometrics, 35: (3), p Montgomery, D.C., Borror, C.M. and Stanley, J.D., (1997). “Some Cautions in the Use of Plackett-Burman Designs,” Quality Engineering, 10, 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, Hartley, H. O. (1959), “Smallest composite design for quadratic response surfaces,” Biometrics 15, Khuri, A. I. (1988), “A Measure of Rotatability for Response Surface Designs,” Technometrics, 30, 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. 28