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Stat 321 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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Stat 321 A Taguchi Case Study

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  1. Stat 321 A Taguchi Case Study Experiments to Minimize Variance

  2. 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

  3. 8-trial, full factorial • 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

  4. See the design matrix Note the factorial in V and W factors in each row of the main design.

  5. 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.

  6. 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

  7. 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.

  8. Conclusions from experiment • Settings at low for Filler Type (A), high for Rubber Quality (B), and low for Pre-Treatment (C) maximize wear resistance and minimize variability. • When settings to optimize mean response and variance conflict, trade-offs must be made.

  9. The Good and Bad of Taguchi • The Great Debate of 1985-1992 • "The Ten Top Triumphs and Tragedies of Taguchi."

  10. 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

  11. 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.

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