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5.   Process Improvement - Detailed Table of Contents  [5.]



  1. Introduction  [5.1.]
    1. What is experimental design?  [5.1.1.]
    2. What are the uses of DOE?  [5.1.2.]
    3. What are the steps of DOE?  [5.1.3.]

  2. Assumptions  [5.2.]
    1. Is the measurement system capable?  [5.2.1.]
    2. Is the process stable?  [5.2.2.]
    3. Is there a simple model?  [5.2.3.]
    4. Are the model residuals well-behaved?  [5.2.4.]

  3. Choosing an experimental design  [5.3.]
    1. What are the objectives?  [5.3.1.]
    2. How do you select and scale the process variables?  [5.3.2.]
    3. How do you select an experimental design?  [5.3.3.]
      1. Completely randomized designs  [5.3.3.1.]
      2. Randomized block designs  [5.3.3.2.]
        1. Latin square and related designs  [5.3.3.2.1.]
        2. Graeco-Latin square designs  [5.3.3.2.2.]
        3. Hyper-Graeco-Latin square designs  [5.3.3.2.3.]
      3. Full factorial designs  [5.3.3.3.]
        1. Two-level full factorial designs  [5.3.3.3.1.]
        2. Full factorial example  [5.3.3.3.2.]
        3. Blocking of full factorial designs  [5.3.3.3.3.]
      4. Fractional factorial designs  [5.3.3.4.]
        1. A 23-1 design (half of a 23)  [5.3.3.4.1.]
        2. Constructing the 23-1 half-fraction design  [5.3.3.4.2.]
        3. Confounding (also called aliasing)  [5.3.3.4.3.]
        4. Fractional factorial design specifications and design resolution  [5.3.3.4.4.]
        5. Use of fractional factorial designs  [5.3.3.4.5.]
        6. Screening designs  [5.3.3.4.6.]
        7. Summary tables of useful fractional factorial designs  [5.3.3.4.7.]
      5. Plackett-Burman designs  [5.3.3.5.]
      6. Response surface designs  [5.3.3.6.]
        1. Central Composite Designs (CCD)  [5.3.3.6.1.]
        2. Box-Behnken designs  [5.3.3.6.2.]
        3. Comparisons of response surface designs  [5.3.3.6.3.]
        4. Blocking a response surface design  [5.3.3.6.4.]
      7. Adding centerpoints  [5.3.3.7.]
      8. Improving fractional factorial design resolution  [5.3.3.8.]
        1. Mirror-Image foldover designs  [5.3.3.8.1.]
        2. Alternative foldover designs  [5.3.3.8.2.]
      9. Three-level full factorial designs  [5.3.3.9.]
      10. Three-level, mixed-level and fractional factorial designs  [5.3.3.10.]

  4. Analysis of DOE data  [5.4.]
    1. What are the steps in a DOE analysis?  [5.4.1.]
    2. How to "look" at DOE data  [5.4.2.]
    3. How to model DOE data  [5.4.3.]
    4. How to test and revise DOE models  [5.4.4.]
    5. How to interpret DOE results  [5.4.5.]
    6. How to confirm DOE results (confirmatory runs)  [5.4.6.]
    7. Examples of DOE's  [5.4.7.]
      1. Full factorial example  [5.4.7.1.]
      2. Fractional factorial example  [5.4.7.2.]
      3. Response surface model example  [5.4.7.3.]

  5. Advanced topics  [5.5.]
    1. What if classical designs don't work?  [5.5.1.]
    2. What is a computer-aided design?  [5.5.2.]
      1. D-Optimal designs  [5.5.2.1.]
      2. Repairing a design  [5.5.2.2.]
    3. How do you optimize a process?  [5.5.3.]
      1. Single response case  [5.5.3.1.]
        1. Single response: Path of steepest ascent  [5.5.3.1.1.]
        2. Single response: Confidence region for search path  [5.5.3.1.2.]
        3. Single response: Choosing the step length  [5.5.3.1.3.]
        4. Single response: Optimization when there is adequate quadratic fit  [5.5.3.1.4.]
        5. Single response: Effect of sampling error on optimal solution  [5.5.3.1.5.]
        6. Single response: Optimization subject to experimental region constraints  [5.5.3.1.6.]
      2. Multiple response case  [5.5.3.2.]
        1. Multiple responses: Path of steepest ascent  [5.5.3.2.1.]
        2. Multiple responses: The desirability approach  [5.5.3.2.2.]
        3. Multiple responses: The mathematical programming approach  [5.5.3.2.3.]
    4. What is a mixture design?  [5.5.4.]
      1. Mixture screening designs  [5.5.4.1.]
      2. Simplex-lattice designs  [5.5.4.2.]
      3. Simplex-centroid designs  [5.5.4.3.]
      4. Constrained mixture designs  [5.5.4.4.]
      5. Treating mixture and process variables together  [5.5.4.5.]
    5. How can I account for nested variation (restricted randomization)?  [5.5.5.]
    6. What are Taguchi designs?  [5.5.6.]
    7. What are John's 3/4 fractional factorial designs?  [5.5.7.]
    8. What are small composite designs?  [5.5.8.]
    9. An EDA approach to experimental design  [5.5.9.]
      1. Ordered data plot  [5.5.9.1.]
      2. DOE scatter plot  [5.5.9.2.]
      3. DOE mean plot  [5.5.9.3.]
      4. Interaction effects matrix plot  [5.5.9.4.]
      5. Block plot  [5.5.9.5.]
      6. DOE Youden plot  [5.5.9.6.]
      7. |Effects| plot  [5.5.9.7.]
        1. Statistical significance  [5.5.9.7.1.]
        2. Engineering significance  [5.5.9.7.2.]
        3. Numerical significance  [5.5.9.7.3.]
        4. Pattern significance  [5.5.9.7.4.]
      8. Half-normal probability plot  [5.5.9.8.]
      9. Cumulative residual standard deviation plot  [5.5.9.9.]
        1. Motivation: What is a Model?  [5.5.9.9.1.]
        2. Motivation: How do we Construct a Goodness-of-fit Metric for a Model?  [5.5.9.9.2.]
        3. Motivation: How do we Construct a Good Model?  [5.5.9.9.3.]
        4. Motivation: How do we Know When to Stop Adding Terms?  [5.5.9.9.4.]
        5. Motivation: What is the Form of the Model?  [5.5.9.9.5.]
        6. Motivation: Why is the 1/2 in the Model?  [5.5.9.9.6.]
        7. Motivation: What are the Advantages of the LinearCombinatoric Model?  [5.5.9.9.7.]
        8. Motivation: How do we use the Model to Generate Predicted Values?  [5.5.9.9.8.]
        9. Motivation: How do we Use the Model Beyond the Data Domain?  [5.5.9.9.9.]
        10. Motivation: What is the Best Confirmation Point for Interpolation?  [5.5.9.9.10.]
        11. Motivation: How do we Use the Model for Interpolation?  [5.5.9.9.11.]
        12. Motivation: How do we Use the Model for Extrapolation?  [5.5.9.9.12.]
      10. DOE contour plot  [5.5.9.10.]
        1. How to Interpret: Axes  [5.5.9.10.1.]
        2. How to Interpret: Contour Curves  [5.5.9.10.2.]
        3. How to Interpret: Optimal Response Value  [5.5.9.10.3.]
        4. How to Interpret: Best Corner  [5.5.9.10.4.]
        5. How to Interpret: Steepest Ascent/Descent  [5.5.9.10.5.]
        6. How to Interpret: Optimal Curve  [5.5.9.10.6.]
        7. How to Interpret: Optimal Setting  [5.5.9.10.7.]

  6. Case Studies  [5.6.]
    1. Eddy Current Probe Sensitivity Case Study  [5.6.1.]
      1. Background and Data  [5.6.1.1.]
      2. Initial Plots/Main Effects  [5.6.1.2.]
      3. Interaction Effects  [5.6.1.3.]
      4. Main and Interaction Effects: Block Plots  [5.6.1.4.]
      5. Estimate Main and Interaction Effects  [5.6.1.5.]
      6. Modeling and Prediction Equations  [5.6.1.6.]
      7. Intermediate Conclusions  [5.6.1.7.]
      8. Important Factors and Parsimonious Prediction  [5.6.1.8.]
      9. Validate the Fitted Model  [5.6.1.9.]
      10. Using the Fitted Model  [5.6.1.10.]
      11. Conclusions and Next Step  [5.6.1.11.]
      12. Work This Example Yourself  [5.6.1.12.]
    2. Sonoluminescent Light Intensity Case Study  [5.6.2.]
      1. Background and Data  [5.6.2.1.]
      2. Initial Plots/Main Effects  [5.6.2.2.]
      3. Interaction Effects  [5.6.2.3.]
      4. Main and Interaction Effects: Block Plots  [5.6.2.4.]
      5. Important Factors: Youden Plot  [5.6.2.5.]
      6. Important Factors: |Effects| Plot  [5.6.2.6.]
      7. Important Factors: Half-Normal Probability Plot  [5.6.2.7.]
      8. Cumulative Residual Standard Deviation Plot  [5.6.2.8.]
      9. Next Step: DOE Contour Plot  [5.6.2.9.]
      10. Summary of Conclusions  [5.6.2.10.]
      11. Work This Example Yourself  [5.6.2.11.]

  7. A Glossary of DOE Terminology  [5.7.]

  8. References  [5.8.]
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