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


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


State of the art approach use of fractional factorials
State-of-the-Art Approach – Use of Fractional Factorials

Generator: D = ABC

Resolution IV design


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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