1. Lecture 15 Today: Finish FFSP designs, 10.1-10.5 Next day: 10.6-10.9 Read 10.2-10.3!!!

2. Robust Parameter Design Robust parameter design is an experimentation technique which aims to reduce system variation and also optimize the mean system response Idea is to use control factors to make the system robust to the influences of noise factors

3. Example: Leaf Spring Experiment (p. 438) Experiment was conducted to investigate the impact of a heat treatment process on truck leaf springs where the target height of the springs is 8 inches Experiment considered 5 factors, each at 2 levels: –B: High heat treatment –C: Heating time –D: Transfer time –E: Hold down time –Q: Quench oil temperature In regular production Q is not controllable, but can be in the experiment

4. Example: Leaf Spring Experiment (p. 438) 2 5-1 fractional factorial design was performed: I=BCDE Experiment has 3 replicates

5. Noise Factors Noise factors are factors that impact the system response, but in practice are not controllable Examples include environmental factors, differing user conditions, variation in process parameter settings, … Example: refrigerators are manufactured so that the interior temperature remains close to some target Section 10.3 discusses different types of noise factors…please read

6. Variance Reduction Via Parameter Design Let x denote the control factor settings and z denote the noise factor settings Relationship between the system response and the factors: y = f(x,z) If noise factors impact the response, then variation in the levels of z will transmit this variance to the response, y If some noise and control factors interact, can potentially adjust levels of control factors to dampen impact of noise factor variation

7. Variance Reduction Via Parameter Design Suppose there is one noise factor and two control factors What is variance of y in practice? What does this imply?

8. Cross Array Strategy We will consider two types of design/analysis techniques for robust parameter design The first one uses location-dispersion modeling (e.g., have a model for the mean response and another for the variance) similar to the epitaxial layer growth experiment in Chapter 3 The design strategy for this technique is based on a cross array

9. Cross Array Strategy Consider the leaf spring example We can view this experiment as the combination of two separate experimental designs –Control array: design for the control factors –Noise array: design for the noise factors Cross array: design consisting of all level combinations between the control array and the noise array If there are N 1 runs in the control array and N 2 trials in the noise array, then the cross array has N 1 N 2 trials

10. Cross Array Strategy The responses are modeled using the location-dispersion approach The models include ONLY the control factors At each control factor setting, and are used as measures of location and dispersion Factors that impact the mean are called location factors and those that impact the variance are dispersion factors Location factors that are not dispersion factors are called adjustment factors

11. Example: Leaf Spring

14. Location Model: Dispersion Model: Level settings:

15. Example: Leaf Spring Location Model: Dispersion Model: Level settings: