Transcript Stat 321 - 5/5/99 - A Taguchi Case Study

Stat 321
A Taguchi Case Study
Experiments to
Minimize Variance
Rubber Tire Study
with Inner and Outer Arrays
• Include environmental variables as
noise factors in the replicates - the outer
array
• Include our usual control factors as the
inner array
8-trial, full factorial
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Factor A - Type of filler
Factor B - Quality of Rubber
Factor C - Method of pre-treatment
Outer Array Factor V - Air pressure
Outer Array Factor W - Ambient
temperature
• Response is wear resistance
See the design matrix
Note the factorial in V and
W factors in each row of
the main design.
Analysis of responses
• Y-bar= ave of 4 results per trial (row)
• Y-bar is analyzed to optimize the
mean response
• log s= natural log of row standard
deviation
• Log s is analyzed to minimize the
variance.
Analysis of significant factors
for variance
• Factor C is significant for standard
deviation, as is the BxC interaction
(demonstrated by the normal plot).
• High level of Rubber (B) with low level
of Pre-Treatment (C) gives the best
standard deviation
Analysis of significant factors
for mean response
• Filler Type (A) and Rubber Quality (B)
have significant effect on wear
resistance, by F-tests (not clear on
normal plot).
• These F-tests are conservative - less
likely to see effects as significant. Why?
• Wear resistance is maximized with low
Filler Type and high Rubber Quality.
Conclusions from experiment
• Settings at low for Filler Type (A), high
for Rubber Quality (B), and low for PreTreatment (C) maximize wear
resistance and minimize variability.
• When settings to optimize mean
response and variance conflict, tradeoffs must be made.
The Good and Bad of Taguchi
• The Great Debate
of 1985-1992
• "The Ten Top
Triumphs and
Tragedies of
Taguchi."
Taguchi’s contributions
• The quality loss function - poor quality is
a cost to society
• Focus on minimizing variance (outer
array method)
• Robustness designed in to counteract
environmental and component variation
• Rebirth of factorial experimentation from agriculture to engineering
Taguchi’s weaknesses
• Signal-to-noise ratios don't separate the
signal and the noise.
• 3-level factors as a default waste
experiment trials.
• Interactions are assumed to be known
ahead of experimentation.
• Pick-the-winner analysis ignores
statistical significance.