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Optimization of
Paint Formulations
with the Taguchi Method.
Drs. Rogier van Duin
Thursday 1st February 2007
High Throughput Formulation Techniques
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Content Overview
Introduction RvD and Duvaro
Research Methodologies
Introduction to Taguchi Method
Example
Discussion
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1989 : M.Sc. Physical Chemistry
Introduction Drs. Rogier van Duin
1989 : Philips, NL
1991 : DSM Resins, NL
1994 : ICI Packaging Coatings, D
2001 : Valspar, CH
2004 : Stahl, NL
2007 : Duvaro, NL
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Introduction Duvaro
Products and Services DUVARO
• Business Solutions, Due Diligence
• New Product Development & Innovation
• Human Resource Management
• Career Development & Coaching
• Interim Management
• Product Stewardship: REACH
• Industrial and Technical Marketing
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Research Methodologies
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Whom of you are familiar with:
Trial and Error ?
One Factor at the Time ?
Full or Fractional Factorial Design ?
Taguchi ?
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Please Raise Hands
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Research approaches trial & error
Classically R&D work with coatings involves a fair amount of
• trial & error experimentation,
• empirical techniques,
• and “black-box” approaches to interpret results.
“Panic Mode”
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Trial & Error experimentation
Based upon knowledge,
just give it a shot…
�Fast result
�Frustration
�Poor Understanding
� Low Chance of finding Optimum
�Accepting (temporary) solution
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Research approaches trial & error
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The classical view of experimentation is to change one factor at a time, run the experiment, observe the results, and move on to the next factor.
This approach has several drawbacks:� It takes much longer and� uses up more resources;
� the optimum combination of all variables may never be revealed;
� and the interaction between factors may never be revealed.
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2
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Research approaches 1 factor....
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Research approaches Simplex method
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2
More structured, danger of sub optimization
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Research approaches RSM
Response Surface Method
Choose hypothetical model
peak
saddle
http://www.scielo.br/scielo.php?pid=S0101-20611999000200025&script=sci_arttext
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Effect of the pH and the glycerol concentration on the rupture of a bio-film
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Choose hypothetical model
Research approaches full factorial
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11 1 8
1 1 -1 7
1 -1 1 6
1 -1 -1 5
-1 1 1 4
-1 1 -1 3
-1 -1 1 2
-1 -1 -1 1
X3 X2 X1 run
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DOE versus Taguchi
Design of Experiments
3 variables at 2 levels : 23 = 8 experiments
Taguchi
7 variables at 2 levels: 8 experiments !
With same effort more information; efficient !
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Taguchi made a significant contribution by adapting fractional factorial
orthogonal arrays to experimental design so that time and cost of experimentation are reduced while validity and reproducibility are
maintained.
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factor interactions
run A B C AB AC BC ABC
1 -1 -1 -1 1 1 1 -1
2 1 -1 -1 -1 -1 1 13 -1 1 -1 -1 1 -1 1
4 1 1 -1 1 -1 -1 -1
5 -1 -1 1 1 -1 -1 1
6 1 -1 1 -1 1 -1 -1
7 -1 1 1 -1 -1 1 -1
8 1 1 1 1 1 1 1Taguchi col no 4 2 1 6 5 3 7
run 1 2 3 4 5 6 7
1 1 1 1 1 1 1 1
2 1 1 1 2 2 2 23 1 2 2 1 1 2 2
4 1 2 2 2 2 1 1
5 2 1 2 1 2 1 2
6 2 1 2 2 1 2 1
7 2 2 1 1 2 2 1
8 2 2 1 2 1 1 2classical col no C B BC A AC AB ABC
A classical 23 design, to investigate the effects of factors A,B, and C, and also the 3
associated two way interactions, and the single three way interaction.
Classical 23 Design
Taguchi L8 Array
A Taguchi L8 array, to investigate the effects of up to 7 factors in 8 runs. This corresponds to the same classical design above.
DOE versus Taguchi
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Unlike classical experimentation, Taguchi experiments can provide the following benefits:
• Many factors can be examined simultaneously.
• Some input factors that cannot be controlled, which are called noise factors, can influence the output; however, other input factors can then be controlled to reduce the effect of the “noise.”
• In-depth statistical knowledge is not necessary to perform these tests and reap their benefits.
• Relatively few experiments can look at a large number of factors and separate the trivial from the important.
• In most cases, quality and reliability can be improved without increasing costs.
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DOE versus Taguchi
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Dr. W.E. Deming once said:
“Any technique is useful as
long as the user understands
its limitations”.
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Introduction to Taguchi
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Born in Japan, 1924
Credited for starting the “Robust Design” movement
in Japan in 1950s.
In 1964 he became professor of engineering at Aoyama Gakuin University, Tokyo.
In the eighties and nineties, he introduced Taguchi method to Bell Labs, Ford Motor Company, Xerox
and AT&T.
Collaboration with Yuin Wu and Madhav Phadke.
Since 1982 Taguchi has been an advisor to the Japanese Standards Institute and executive director
of the American Supplier Institute, an international consulting organization.
Dr. Genichi Taguchi
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http://en.wikipedia.org/wiki/Genichi_Taguchi
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The Taguchi method grabs a quality
problem by the throat.
It goes directly to the basic physics
and thermodynamics of ...,
whatever-that ’s causing trouble,
and solves the problem during the
early design phase.
What experts say about Taguchi
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€
Design
€ € € € €
Product Customer
€ € € € € € € € € € € € € €
Product Consumer
Cost increases when defect is passed
along supply chain
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Taguchi Link with NPD:
Focus on Early Stage
Development
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System
Design
Parameter
Design
Tolerance
Design
Generating and pre-selection of new ideas, concept and free scoping.
Innovation
Creativity
Robust Design
Cost Reduction
Concept: control, signal and noise factors optimization. Parameter
Design experiments should be conducted with low-cost alternatives to present design
settings.
Reduce VariabilityWhich tolerance to tighten.
Development Stages in Taguchi
??: Where do you think lies the partition in % for above design phases in the West compared to the East ?
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“Six sigma yields parts that
meet specs, while Taguchi
produces parts that avoid
failure.
The six-sigma process is okay,
but the Taguchi method is
more robust both in its logic
and its methodology."
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Optimization of Paint Formulations with the Taguchi Method
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Taguchi Quality Loss Function
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Classical: black / white approach
Quality Loss = Loss Quality Loss = Loss
to Society quantifiedto Society quantified
through through ““Quality Quality
Loss FunctionLoss Function””
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Taguchi: dealing with Interactions
Taguchi:Factors are preferred above
interactions.
Reason: in many cases one or more factors are forgotten.
Recommendation: Screening designs. Interactions are leveled out over all
factors.
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As many factors as possible should be identified to
enhance improvement potential. Control factors are usually tested at two or three levels in orthogonal array
experiments.
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Taguchi L12 screening design
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Statisticians comment:
Taguchi assumes most interactions are small and those that
aren’t are known ahead of time.
�He claims that it is possible to eliminate these interactions either by correctly specifying the response
and design factors or by using a sliding setting approach to those factor levels.
What experts say about Taguchi
These designs are very useful for economically detecting large main effects, assuming all interactions are negligible
when compared with the few important main effects.
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What experts say about Taguchi
Switch to factorSwitch to factorPreference at
Weak
Interactions
Use Confirmation Run as validation
assignassignPreference at Strong
Interactions
Switch to factorassignPreference at Medium
Interactions
Rather factors than interactions in early stage
When in doubt, assign interactions
Interactions
TaguchiClassic
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What experts say about Taguchi
My comment:
Taguchi very user friendly;
� It doesn’t require lots of statistical knowledge.
� The design can be tailor-made upon your specific situation.
� Robustness by simulating noise.
� Especially with new technology no “blockage of
experience.”
� Fast and reliable, consistent results.
In over 500 Taguchi experiments more than 2/3 were successful in either generating knowledge or solving the
problem / generating a new product.
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Example
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Yellowing Hot Melt
Problem:
Existing combination of anti oxidants do not preventHot Melt from yellowing (In the dark).
System uses following combinations of anti-oxidants:
Primary Anti Oxidant (pAO)Secondary Anti Oxidant (sAO)
Hindered Amine Light Stabilisator (HALS)
pAO + sAO
pAO + sAO + HALSpAO + HALS
Maximum Dose
pAO: 0.1%sAO: 0.2%
HALS: 0.1%
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Yellowing Hot Melt
Solution:
Use for the combinations an empty level in the factor.
Primary Anti Oxidant (pAO)pAO1, pAO2, pAO3, pAO4 df=3
Secondary Anti Oxidant (sAO)
sAO1(empty), sAO2, sAO3, sAO4 df=3
Hindered Amine Light Stabilisator (HALS)
HALS1(empty), HALS2, HALS3, HALS4 df=3
average df=1:Σdf=10Dose Level 1 Level 2
pAO: 0.025% 0.075%sAO: 0.05% 0.15%
HALS: 0.025% 0.075%
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Yellowing Hot Melt
2314416
1423415
4132414
3241413
3124312
4213311
1342310
243139
123428
214327
341226
432125
444414
333313
222212
111111
emptyemptyHALSsAOpAO
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Yellowing Hot Melt
200 Hazen =1 Gardner
low conc pAO sAO HALS 1w eek 3w eek s 5w eek s 1w eek 3w eek s 5w eeks
1 1 1 1 80 2 5 90 1 5
2 1 2 2 90 1 4 110 1 4
3 1 3 3 80 2 4 90 110 3
4 1 4 4 200 2 5 110 2 4
5 2 1 2 80 2 3 70 110 2
6 2 2 1 80 1 4 70 110 3
7 2 3 4 60 1 4 60 80 2
8 2 4 3 80 80 1 30 90 100
9 3 1 3 70 100 2 80 90 120
10 3 2 4 90 2 5 100 1 5
11 3 3 1 50 1 2 60 110 2
12 3 4 2 200 2 5 1 1 4
13 4 1 4 70 2 5 80 110 3
14 4 2 3 80 90 110 80 80 100
15 4 3 2 70 100 2 60 1 3
16 4 4 1 90 2 5 90 1 4
low concen t rat ion h igh concen t rat ion
Number of experiments: 2 x 16 + 2 confirmation runs of the PC.
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Yellowing Hot Melt
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F1 low, F2 high concentration
B1, C1 empty (no sAO, HALS)
Paper champion:
A2 B3 C3
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Yellowing Hot Melt
before afterConfirmation Run of
the Paper Champion
After 13 years still stable:
Robust Design!
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Yellowing Hot Melt
Epilogue (1):
By solving the yellowing problem on short notice, the
customer could be re-supplied without line-stop.
The new anti-oxidation system is not only more effective, but also less expensive.
The yellowing decreased by a factor 5 – 10, depending on the binder system.
Within a short period an enormous knowledge build up
had taken place.
Commitment through all company layers; especially Marketing & Sales – Research & Development.
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Yellowing Hot Melt
Epilogue (2):
The binder system became more stable in production
(less variation; more ROBUST Taguchi would call it).
This significant improvement revolved a potential claim
into increased business.
Total time invested: approx. 60 hours = 4.5k€The Taguchi experiment delivered 500k€.
After the paper champion, a second smaller experimental
design was set up, which let to the discovery of another important factor. Which originally was hiding in the “noise”.
After ½ year the turn-over sharply rose to access to new,
higher quality demanding markets.
Thank you for your time and attention
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