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Lecture 16

Lecture 16. Today: 10.6-10.9 Next day:. Two-Step Optimization Procedures. Nominal the best problem: Select the levels of the dispersion factors to minimize the dispersion The select the levels of the adjustment factors to move the process on target Larger (Smaller) the better problem:

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Lecture 16

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  1. Lecture 16 • Today: 10.6-10.9 • Next day:

  2. Two-Step Optimization Procedures • Nominal the best problem: • Select the levels of the dispersion factors to minimize the dispersion • The select the levels of the adjustment factors to move the process on target • Larger (Smaller) the better problem: • Select levels of location factors to optimize process mean • Select levels of dispersion factors that are not location factors to minimize dispersion • Leaf Spring Example was a nominal the best problem

  3. Response Modeling • There may be several noise factors and control factors in the experiment • The cross array approach identifies control factors to help adjust the dispersion and location models, but does not identify which noise factors interact with which control factors • Cannot deduce the relationships between control and noise factors • The response model approach explicitly model both control and noise factors in a single model (called the response model)

  4. Response Modeling • Steps: • Model response, y, as a function of both noise and control factors (I.e., compute regression model with main effects and interactions of both types of factors) • To adjust variance: • make control by noise interaction plots for the significant control by noise interactions. The control factor setting that results in the flattest relationship gives the most robust setting. • construct the variance model, and choose control factor settings that minimize the variance

  5. Example: Leaf Spring Experiment (p. 438) • 25-1 fractional factorial design was performed: I=BCDE • Experiment has 3 replicates

  6. Example: Leaf Spring Experiment (p. 438) • 25-1 fractional factorial design was performed: I=BCDE

  7. Example: Leaf Spring Experiment (p. 438)

  8. Example: Leaf Spring Experiment (p. 438)

  9. Example: Leaf Spring Experiment (p. 438) • Response Model:

  10. Example: Leaf Spring Experiment (p. 438)

  11. Example: Leaf Spring Experiment (p. 438) • Variance Model:

  12. Design Strategy for the Response Model

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