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
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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
Partition Design
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Partition Design Assumptions

• Process/Product Knowledge required
• Screening Experiment required
• Resources limited, minimize runs
• Sparsity-of-Effect Principle

6
Partition Design Methodology

• 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

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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

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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)

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Step 1 Perform Screening Experiment

• Process 1
• Significant Factors
• Factor A
• Factor B

• Process 2
• Significant Factors
• Factor C
• Factor D

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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

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Step 2 Construct Partition Design

• First-order Design (Res III or Saturated)
• Orthogonal
• D-optimality
• Minimize Alias Confounding

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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
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Step 3 Perform Partition Design Experiment

• Planning is key
• Requires increased coordination between process
  steps
• Identification of Outputs and Inputs

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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

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Step 4a Select Significant Effects
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Step 4a Select Significant Effects
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Step 4b Build Empirical Model
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Step 4cCalculate 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
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Step 4 Partition Analysis

• Repeat for Second Partition
• Select Significant Effects
• Build Empirical Model
• Calculate Partition Intercept Response

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Step 4dSelect Significant Effects for Intercept
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Step 5Build Final Empirical Model
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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

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Case Study Biogen IDEC Partition Design
Experimental
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
1
2
k
20 CEX eluate pools
20 Protein-A eluate pools

. . .

. . .

. . .
Protein-A
Harvest
CIEX

. . .

. . .

. . .

z

z

z

z

z

z

z

z

z
1
2
r
1
2
r
1
2
r
Uncontrollable factors
Uncontrollable factors
Uncontrollable factors

• 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

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Partition Design Designs
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CIEX Step HCP ANOVA Comparison Main Effects
Partition Model Results
Traditional Model Results
Input Parameter of Total Sum of Squares
Harvest pH 32.6
Pro A Wash I Conc. 17.7
Harvest pH Pro A Wash I 15.6
CIEX Elution pH 10.1
Harvest pH CIEX Elution pH 8.8
Pro A Wash I. CIEX Elution pH 4.6
CIEX Load Capacity 3.9
Pro A Wash I. Conc. CIEX Elution NaCl 1.8
CIEX Elution NaCl 1.5
Harvest pH CIEX Elution NaCl 1.2
CIEX Elution NaCl CIEX Elution pH 0.2
R2 0.99
Adjusted R2 0.99
Predicted R2 0.96
Input Parameter of Total Sum of Squares
Load HCP f(Harvest pH, ProA Wash I) 83.3
CIEX Elution pH 6.6
Load HCP2 5.8
Load HCP Elution pH 1.6
CIEX Elution NaCl 1.1
CIEX Elution pH2 0.7
CIEX Elution NaCl CIEX Elution pH 0.5
Load HCP CIEX Elution NaCl 0.2
CIEX Load Capacity 0.1
R2 0.96
Adjusted R2 0.95
Predicted R2 0.92

• Partition model identified same significant main
  factors and their relative rank in significance

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CIEX Step HCP ANOVA Comparison Interactions
Partition Model Results
Traditional Model Results
Input Parameter of Total Sum of Squares
Harvest pH 32.6
Pro A Wash I Conc. 17.8
Harvest pH Pro A Wash I conc 15.6
CIEX Elution pH 10.1
Harvest pH CIEX Elution pH 8.8
Pro A Wash I. Conc. CIEX Elution pH 4.6
CIEX Load Capacity 3.9
ProA Wash 1. CIEX Elution NaCl 1.8
Elution NaCl 1.5
Harvest pH CIEX Elution NaCl 1.2
CIEX Elution NaCl CIEX Elution pH 0.2
Input Parameter Sum of Squares
Load HCP f(A,C) 83.3
CIEX Elution pH 6.6
Load HCP2 5.8
Load HCP CIEX Elution pH 1.6
Elution NaCl 1.1
Elution pH2 0.7
Elution NaCl CIEX Elution pH 0.5
Load HCP CIEX Elution NaCl 0.2
SPXL Load Capacity (mg/ml) 0.1

• Partition model able to identify interactions
  between process steps

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Summary of Partition Designs
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 1
Process 2
Process 3
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

• 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

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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.