post fractionated strip block designs a tool for robustness applications and multistage processes
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Post-Fractionated Strip-Block Designs: A Tool for Robustness Applications and Multistage Processes. Carla A. Vivacqua [email protected] University of Wisconsin-Madison Federal University of Rio Grande do Norte-Brazil S øren Bisgaard University of Massachusetts-Amherst

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post fractionated strip block designs a tool for robustness applications and multistage processes

Post-Fractionated Strip-Block Designs: A Tool for Robustness Applications and Multistage Processes

Carla A. Vivacqua

[email protected]

University of Wisconsin-Madison

Federal University of Rio Grande do Norte-Brazil

Søren Bisgaard

University of Massachusetts-Amherst

Harold J. Steudel

University of Wisconsin-Madison

outline
Outline
  • Motivation
  • Research Question
  • Battery Cells Case Study
  • New Arrangement: Post-Fractionated Strip-Block Designs
  • Conclusions
motivation
Motivation
  • Competitive environment requires:
    • Design of high-quality products and processes at low cost
  • Design of experiments (DOE) plays a critical role
research question
Research Question
  • How to reduce costs of experimentation?
    • Robust Design
      • Products insensitive to different sources of variation
    • Multistage Processes
slide5

Battery Cells Case Study

Begin

Task 1

  • Defective rate: 5%
  • Cause of cells rejection: high open circuit voltage (OCV)
  • Consequences of high OCV: self-discharging, leading to low performance or dead cells.

Task 2

Assembly

Process

Task n

Storage Process

End

process characteristics
Process Characteristics
  • Two shifts for production
  • One storage room
  • Storage cycle: at least five days
  • Six factors for investigation
    • Assembly process: A, B, C, D
    • Storage process: E, F
approach 1
Approach 1
  • Completely randomized design
  • 26 = 64 independent trials
  • 64 changes in assembly configuration
    • Could not be run in one shift
  • 64 changes in storage conditions
    • Data collection: 64 * 5 = 320 days
approach 2
Approach 2

}

22 full factorial design

  • Advantages:
    • only 16 changes in the assembly configuration
    • only 4 changes in the storage configuration

24 full factorial design

16 trials

scenario
Scenario
  • Space restrictions in storage room
  • Only 8 sub-lots can be placed in the storage room simultaneously
new approach post fractionated strip block design
New Approach: Post-Fractionated Strip-Block Design

Generator: EF = ABCD

Resolution VI design

post fractionated strip block design 2
Post-Fractionated Strip-Block Design (2)

Generators: E = ABC, F = BCD

Reduces to a split-plot design

maximum post fractionation order
Maximum Post-Fractionation Order
  • Base strip-block design: 2k-p x 2q-r
  • Maximum value for post-fractionation order to preserve the strip-block structure:

f = min(k-p, q-r) - 1.

Ex.: 24 x 22 base design

f = min(4, 2) – 1 = 2 – 1 = 1

analysis of post fractionated strip block designs
Analysis of Post-Fractionated Strip-Block Designs
  • Compute main effects and interactions
  • Not all effects with same precision
  • Group effects with same variance
  • Separate analyses for each stratum
  • Four different strata
contrast estimates

q-r = 2 basic generators of column design

k-p = 4 basic generators of row design

Remaining Contrasts

Contrast Estimates

f = 1 basic generator of post-fraction

conclusions
Conclusions
  • Post-fractionated strip-block designs
    • Cost-effective method to gather knowledge about products and processes
    • Attention to conduct appropriate analysis
before vs after implementation
Before vs. After Implementation

New percentage of rejects  0.92%

Improvement of 82%

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