dema2008 post-fractionated strip-block designs with applications to robust design and multistage...
TRANSCRIPT
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DEMA2008
Post-Fractionated Strip-Block Designs with Applications to Robust Design
and Multistage Processes
Carla A. VivacquaUniversidade Federal do Rio Grande do Norte (UFRN) - Brazil
Søren BisgaardUniversity of Massachusetts Amherst (UMASS) – USA
University of Amsterdam – The Netherlands
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2DEMA2008
Outline
• Introduction:– Strip-block designs– Battery cells case study
• New Arrangement: Post-Fractionated Strip-Block Design
• Analysis• Conclusions
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3DEMA2008
Introduction
• Competitive environment requires:– Design of high-quality products and processes
at low cost
• Six Sigma initiatives:– Design of experiments (DOE) plays a critical
role
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4DEMA2008
Research Question
• How to reduce costs of experimentation? – Robust Design
• Products insensitive to different sources of variation
– Multistage Processes
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5DEMA2008
Project Home
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6DEMA2008
The Problem
• High percentage of rejected batteries
• Annual losses of over $154,000
• 2 millions batteries scraped annually
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7DEMA2008
Customer Requirements
• High performance batteries
• Specification limits for the critical to quality issues:– Open Circuit Voltage (OCV) [1.00V, 1.38V]– Impedance [2Ω, 8Ω]
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8DEMA2008
Various Types of Batteries
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
2000/07 2000/08 2000/09 2000/10 2000/11 2000/12 2001/01
Hig
h O
CV
Rej
ects
($)
5A
10U
10SU
312U
312SU
13U
13SU
Total
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9DEMA2008
Battery Cells Case Study
Task 2
Task 1
Task n
Curing Process
End
Begin
AssemblyProcess
• Defective rate: 5%
• Cause of cells rejection: high OCV
• Consequences of high OCV: self-discharging, leading to low performance or dead cells.
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10DEMA2008
Objective
• Identify settings of process variables leading to high quality battery cells– Close to target– Least amount of variation
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11DEMA2008
Process Characteristics
• Two shifts for production• One curing room• Storage cycle: at least five days• Six factors for investigation
– Assembly process: A, B, C, D– Curing process: E, F
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12DEMA2008
Approach 1
• Completely randomized design
• 26 = 64 independent trials
• 64 changes in assembly configuration– Could not be run in one shift
• 64 changes in curing conditions– Data collection: 64 * 5 = 320 days
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13DEMA2008
(16)
(2)
(1)
(4)(3)(2)(1)
Curing Variables (22)
Curing ConditionsAssembly Variables
(24)
Fully Randomized Arrangement
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14DEMA2008
Approach 2
EF
A B C D
Storage VariablesSub-plots
Assembly VariablesWhole-plots
} 22 full factorial design with 16 replicates
24 full factorial design
Requires 16 changes in assembly
configuration
Still requires 64 changes in the storage configuration
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15DEMA2008
(16)
(2)
(1)
(4)(3)(2)(1)
Storage Variables (22 with 16 replicates)Storage ConditionsAssembly
Variables (24)
Run
Split-Plot Design
Whole Plot Sub-Plot
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16DEMA2008
Approach 3
EF
A B C D
Curing VariablesAssembly Variables
} 22 full factorial design
24 full factorial design16 trials
• Advantages:
– only 16 changes in the assembly configuration– only 4 changes in the curing configuration
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17DEMA2008
(16)
(2)
(1)
(4)(3)(2)(1)
Curing Variables (22)Curing ConditionsAssembly
Variables (24)
Run
Strip-Block Design
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18DEMA2008
Strip-Block Experiment
Order E- F- E+ F- E- F+ E+ F+
11 - - - - X X X X15 + - - - X X X X5 - + - - X X X X3 + + - - X X X X9 - - + - X X X X13 + - + - X X X X2 - + + - X X X X12 + + + - X X X X8 - - - + X X X X4 + - - + X X X X1 - + - + X X X X6 + + - + X X X X14 - - + + X X X X7 + - + + X X X X10 - + + + X X X X16 + + + + X X X X
Run
Curing Conditions
Based on Factors E & F
Assembly Factors
A B C D
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19DEMA2008
Scenario
• Space restrictions in storage room
• Only 8 sub-lots can be placed in the storage room simultaneously
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20DEMA2008
State-of-the-Art Approach – Use of Fractional Factorials
- + - + E
A B C D ABCD - - + + F
- - - - + X X X X
+ + - - + X X X X
+ - + - + X X X X
- + + - + X X X X
+ - - + + X X X X
- + - + + X X X X
- - + + + X X X X
+ + + + + X X X X
Row Design
Column Design
Generator: D = ABCResolution IV design
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21DEMA2008
New Approach: Post-Fractionated Strip-Block Design
- + - + E- - + + F
A B C D ABCD + - - + EF- - - - + X X+ - - - - X X- + - - - X X+ + - - + X X- - + - - X X+ - + - + X X- + + - + X X+ + + - - X X- - - + - X X+ - - + + X X- + - + + X X+ + - + - X X- - + + + X X+ - + + - X X- + + + - X X+ + + + + X X
Row Design
Column Design
Generator: EF = ABCDResolution VI design
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22DEMA2008
Post-Fractionated Strip-Block Design (2)
- + - + E
A B C D ABC BCD - - + + F
- - - - - - X
+ - - - + - X
- + - - + + X
+ + - - - + X
- - + - + + X
+ - + - - + X
- + + - - - X
+ + + - + - X
- - - + - + X
+ - - + + + X
- + - + + - X
+ + - + - - X
- - + + + - X
+ - + + - - X
- + + + - + X
+ + + + + + X
Row Design
Column Design
Generators: E = ABC, F = BCDReduces to a split-plot design
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23DEMA2008
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
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24DEMA2008
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
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25DEMA2008
Contrast Estimates
Effect Estimate Effect Estimate Effect Estimate Effect EstimateA -0.00331 E 0.00456 AE -0.00331 EF= ABCD -0.00181
B -0.00169 F -0.03056 AF 0.00131
C 0.00456 BE 0.00331
D 0.00656 BF 0.00244
AB -0.00381 CE -0.00219
AC 0.00369 CF -0.00231
AD -0.00156 DE 0.00256
BC 0.00006 DF 0.00369
BD -0.00294 ABE -0.00031
CD 0.00081 ABF -0.00244
ABC -0.00206 ACE 0.00244
ABD 0.00069 ACF 0.00006
ACD -0.00031 ADE -0.00156
BCD= AEF 0.00006 ADF -0.00169
Row Stratum Column Stratum Interaction Stratum Post-Fraction Stratum
f = 1 generator of post-fraction
k-p = 4 basic factors of row design
Remaining effects
q-r = 2 basic factors of
column design
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26DEMA2008
Variances
2224
)ˆ( RCRfrq
NRVar
2224
)ˆ( RCCfpk
NCVar
2^ 4
)( RCNRCVar
222 224
)ˆ( RCCfpk
Rfrq
NFVar
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27DEMA2008
Results
• Based on the analysis of the OCV mean only and taking into account that the problem is cells with high OCV the recommended levels would be:
A high level (+) B high level (+)
C low level (-) D low level (-)
F high level (+)
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28DEMA2008
Results – cont.• Considering the OCV sub-lot variability
and other variables of interest, the recommended settings are:
A low level (-) B low level (-)
C low level (-) D low level (-)
E low level (-) F high level (+)
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29DEMA2008
Conclusions
• Post-fractionated strip-block designs– Cost-effective method to gather knowledge
about products and processes– Attention to conduct appropriate analysis
• Catalogs of maximum resolution post-fractionated strip-block designs– 16-run and 32-run designs– Up to 11 factors
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30DEMA2008
Summary
• Strip-block experiments: – Reduction of experimentation costs– Easy to execute– Logically suitable to available resources
and restrictions
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31DEMA2008
Before vs. After Implementation
0%
1%
2%
3%
4%
5%
6%
7%
Battery Lot
Pe
rce
nt
Hig
h O
CV
Re
jects
New Stomper
80% reduction on defective rate and 75% reduction on process variability!!!!
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32DEMA2008
Questions?
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33DEMA2008