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

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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 vivacqua_at_cae.wisc.edu University of Wisconsin-Madison – PowerPoint PPT presentation

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


1
Post-Fractionated Strip-Block Designs A Tool
for Robustness Applications and Multistage
Processes
  • Carla A. Vivacqua
  • vivacqua_at_cae.wisc.edu
  • 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

2
Outline
  • Motivation
  • Research Question
  • Battery Cells Case Study
  • New Arrangement Post-Fractionated Strip-Block
    Designs
  • Conclusions

3
Motivation
  • Competitive environment requires
  • Design of high-quality products and processes at
    low cost
  • Design of experiments (DOE) plays a critical role

4
Research Question
  • How to reduce costs of experimentation?
  • Robust Design
  • Products insensitive to different sources of
    variation
  • Multistage Processes

5
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
6
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

7
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

8
Approach 2
Assembly Variables Storage Variables
A B C D E F


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
9
Strip-Block Design
Run Assembly Variables (24) Storage Variables (22) Storage Conditions Storage Variables (22) Storage Conditions Storage Variables (22) Storage Conditions Storage Variables (22) Storage Conditions
Run Assembly Variables (24) (1) (2) (3) (4)
(1)
(2)

(16)
10
Scenario
  • Space restrictions in storage room
  • Only 8 sub-lots can be placed in the storage room
    simultaneously

11
State-of-the-Art Approach Use of Fractional
Factorials
Generator D ABC Resolution IV design
12
New Approach Post-Fractionated Strip-Block
Design
Generator EF ABCD Resolution VI design
13
Post-Fractionated Strip-Block Design (2)
Generators E ABC, F BCD
Reduces to a split-plot design
14
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

15
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

16
Contrast Estimates
k-p 4 basic generators of row design
Remaining Contrasts
f 1 basic generator of post-fraction
17
Variances
18
Conclusions
  • Post-fractionated strip-block designs
  • Cost-effective method to gather knowledge about
    products and processes
  • Attention to conduct appropriate analysis

19
Before vs. After Implementation
New percentage of rejects ? 0.92 Improvement of
82
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