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Maximizing Product Performance: Factorial Experiments Analysis

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28 diapositives · 385 Views · Nov 20, 2013

The impact of material type and temperature on product life in this comprehensive study. Learn to identify robust product materials and analyze complex interactions for optimized results with regression models. Discover how to interpret response surfaces, conduct ANOVA analysis, and extend factorial experiments to more than two factors, with detailed step-by-step guides and practical tools provided.

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  1. Factorial Experiments • Text reference, Chapter 5 • General principles of factorial experiments • The two-factor factorial with fixed effects • The ANOVA for factorials • Extensions to more than two factors • Quantitative and qualitative factors – response curves and surfaces Design & Analysis of Experiments 7E 2009 Montgomery

  2. Some Basic Definitions Definition of a factor effect: The change in the mean response when the factor is changed from low to high Design & Analysis of Experiments 7E 2009 Montgomery

  3. The Case of Interaction: Design & Analysis of Experiments 7E 2009 Montgomery

  4. Regression Model & The Associated Response Surface Design & Analysis of Experiments 7E 2009 Montgomery

  5. The Effect of Interaction on the Response Surface Suppose that we add an interaction term to the model: Interaction is actually a form of curvature Design & Analysis of Experiments 7E 2009 Montgomery

  6. Example 5.1 The Battery Life ExperimentText reference pg. 167 • A = Material type; B = Temperature (A quantitative variable) • What effects do material type & temperature have on life? • 2. Is there a choice of material that would give long life regardless of temperature (a robust product)? Design & Analysis of Experiments 7E 2009 Montgomery

  7. The General Two-Factor Factorial Experiment a levels of factor A; b levels of factor B; n replicates This is a completely randomized design Design & Analysis of Experiments 7E 2009 Montgomery

  8. Statistical (effects) model: Other models (means model, regression models) can be useful Design & Analysis of Experiments 7E 2009 Montgomery

  9. Extension of the ANOVA to Factorials (Fixed Effects Case) – pg. 168 Design & Analysis of Experiments 7E 2009 Montgomery

  10. ANOVA Table – Fixed Effects Case Design-Expert will perform the computations Text gives details of manual computing (ugh!) – see pp. 171 Design & Analysis of Experiments 7E 2009 Montgomery

  11. Design & Analysis of Experiments 7E 2009 Montgomery

  12. Design-Expert Output – Example 5.1 Design & Analysis of Experiments 7E 2009 Montgomery

  13. JMP output – Example 5.1 Design & Analysis of Experiments 7E 2009 Montgomery

  14. Residual Analysis – Example 5.1 Design & Analysis of Experiments 7E 2009 Montgomery

  15. Residual Analysis – Example 5.1 Design & Analysis of Experiments 7E 2009 Montgomery

  16. Interaction Plot Design & Analysis of Experiments 7E 2009 Montgomery

  17. Quantitative and Qualitative Factors • The basic ANOVA procedure treats every factor as if it were qualitative • Sometimes an experiment will involve both quantitative and qualitative factors, such as in Example 5.1 • This can be accounted for in the analysis to produce regression models for the quantitative factors at each level (or combination of levels) of the qualitative factors • These response curves and/or response surfaces are often a considerable aid in practical interpretation of the results Design & Analysis of Experiments 7E 2009 Montgomery

  18. Quantitative and Qualitative Factors A = Material type B = Linear effect of Temperature B2 = Quadratic effect of Temperature AB = Material type – TempLinear AB2 = Material type - TempQuad B3 = Cubic effect of Temperature (Aliased) Candidate model terms from Design- Expert: Intercept A B B2 AB B3 AB2 Design & Analysis of Experiments 7E 2009 Montgomery

  19. Quantitative and Qualitative Factors Design & Analysis of Experiments 7E 2009 Montgomery

  20. Regression Model Summary of Results Design & Analysis of Experiments 7E 2009 Montgomery

  21. Regression Model Summary of Results Design & Analysis of Experiments 7E 2009 Montgomery

  22. Design & Analysis of Experiments 7E 2009 Montgomery

  23. Design & Analysis of Experiments 7E 2009 Montgomery

  24. Design & Analysis of Experiments 7E 2009 Montgomery

  25. Design & Analysis of Experiments 7E 2009 Montgomery

  26. Design & Analysis of Experiments 7E 2009 Montgomery

  27. Design & Analysis of Experiments 7E 2009 Montgomery

  28. Factorials with More Than Two Factors • Basic procedure is similar to the two-factor case; all abc…kn treatment combinations are run in random order • ANOVA identity is also similar: • Complete three-factor example in text, Example 5.5 Design & Analysis of Experiments 7E 2009 Montgomery