RSM

January 8th, 2012

Response Surface Methodology

Stat 579  [ 3 ]  Selected Topics: Response Surfaces

Description: Empirical model building and process optimization using experimental design and statistical modeling. The first half of the course covers building empirical first- and second-order empirical models, (fractional) factorial designs, and process improvement with steepest ascent.  The second half covers advanced topics including robust parameter design and mixture experiments.  A final project requires small teams of students to identify a process of their choosing, improve that process, and document their work in a short final report.

Prerequisite: Stat 540, Stat 545, Math 314
Semesters offered: Special

Fall 2011

Lecture: Stat 579.001, TR 15:30-16:45, SMLC 120
Office hours: Tues 2-3pm and Wed 4-5pm in MSLC 312
email: “Erik B. Erhardt” <erike@stat.unm.edu>, please include “RSM” in subject line
Course grade is wholly homework and project-based.  There are assignments associated with each chapter and one final project.  Homework for a given chapter is due one week from the completion of each chapter.
SAS is available in DSH labs 141 & 143, or you can purchase a 1 year license for $100 for SAS 9.2 for Windows.

Notes

WebCT will have the notes, datasets, code, homework, etc.

SAS Programs

(macro *.mac files are *.sas files, run macro first, then use %[macro_name] to execute the macro)
Table 2.8
Example 3.1

Example 3.2

Example 4.5
Example 6.2
Example 6.3
Example 6.6
Example 6.8 (2nd ed), Box-Cox transform
Example 7.6
Constructing CCDs
Design Evaluation
Example 8.10
Design Augmentation
Example 10.5a
Example 11.1
Example 11.2
Generating Mixture Designs
We will be using SAS’s Macros for the Design and Analysis of Experiments: ADX.

Homework

Please include an organized appendix with code you wrote to manipulate data and perform the analysis.  I should be able to indicate what problem each block of code is associated with and involved commands should be commented with their purpose or what they do.

Chapter 2: (part 1) HW1 2.6, 2.12 SAS.

Chapter 2 (sol): 2.6, 2.12, 2.15, 2.16, 2.20, 2.25.
- Use externally studentized residuals in all residual plots.
- In 2.6 and 2.12 conduct lack-of-fit tests for both models.
- In 2.15 and 2.16 obtain a 95% prediction interval at the indicated values in part (b) also.
- In 2.25 fit the model to the original variables first. Then center the predictors before forming product and square terms and refit the model. What changes?

Chapter 3 (sol): 3.1, 3.6, 3.7, 3.11, 3.12, 3.20, 3.26.
For 3.11 replace part (b) with (d).
For 3.20(c), one of the alternative observations for Rep IV is wrong. Indicate what it should be, then answer the question.
To assess significance use the calibrated Lenth procedure and, where applicable, the Loughin and Noble procedure to assess significance. Use only SMOE or EER to pool errors.

Chapter 4 (sol): 4.1, 4.4, 4.5, 4.7, 4.11, 4.20, 4.23.
Whenever appropriate, use Table 4.11, p. 156, and take the main fraction when designing a 2^(k-p).
- For 4.1, we want a one-half fraction of the 2^4 design (not 2^3).
- For 4.4, (i) show that in order to use the data from Table 4.5, p. 144, your design must at best alias some main effects, (ii) choose the design with second generator I=ABD to analyze.
- For 4.23, the original design in Table 4.13 is a 2^(7-4)III, not a 2^(7-3)III, and the resulting design is a 2^(7-3)IV, not a 2^(8-4)IV.

Chapter 5 (sol): 5.5, 5.7.
For 5.5 make the following changes:
- For part (a), fit the first order model and use the results in parts (b) and (c). However, I think if you were doing this for real, fitting the first order model, or even the first order model with two-way interactions, is a bad idea. Do you agree with me? Back up your answer with some analysis.
- For part (b), use all main effects and make one unit steps.
- For part (c), the constraint makes no sense to me. Tell why. Instead of the given constraint, use this one: x1+x2=-2.7 (remember, these are coded units).
For 5.7 (b) and (c), these are extra credit.

Chapter 6 (sol): 6.1, 6.9 (a), (b), (e-g), 6.14 (a), (c).
- For 6.9 (f), constrain the solution to a radius 1.5 of center.
- For 6.14 (a), Fit full second-order model and don’t bother checking assumptions.
- For 6.14 (c),
- – Use the method I have denoted Method C in class.
- – Take Y1: L=90, T=190; Y2: L=700, T=1300; Y3: L=300, T=500, U=700; Y4: L=50, T=67.5, U=85.
- – Optimize d1: r=0.1; d2: r=0.5; d3: r1=1, r2=0.1; d4: r1=0.2, r2=0.75.
- – Give the value of the desirability function and each response at the optimum. Are the response values within the desired ranges?
- – Use [-2,2] cube for domain of interest.
- – Provide contour plot slices of D through the maximum value.

Chapter 7 (sol): 7.1, 7.2, 7.3, 7.5, 7.7, 7.25.
- For 7.7, confirm that the problem statement is correct. If there is an error/are errors, tell what it is/they are and give the correct solution. (I think there are several There may not be an error.)
- For 7.25, do this for k=6 (1/2 rep) instead of k=5 (1/2 rep).

Chapter 8 (sol): 8.8 (a),(b),(d), 8.12, 8.14, 8.15.
- For 8.12, (c) refer to 8.15.
- For 8.14, add 7 rather than 6 additional design points. Make your list of candidates a sensible one with all points within the unit cube. Use D-efficiency as the criterion. Is the resulting augmented design a standard design? If so, tell what it is.
- For 8.15, do this just for D-optimality. The formula near the middle of page 387 may be useful to you.

Chapter 10 (sol): 10.2, 10.4, 10.7, 10.12.
- For 10.4, (a) use the “pick the winner” strategy in the Taguchi analysis, (b) do a second analysis using y-bar and ln(s^2). Comment on any differences between the two analyses in the conclusions you make.

Project

Final project description – The final project requires small teams of students to improve the flight time of a paper helicopter.  The project consists of planning, designing, conducting, and analyzing an experiment, using appropriate design-of-experiment principles, and then using an optimization strategy to improve the process to a stable optimum.  Outcomes include a written project report with a final class presentation, as well as a competition between teams and the professor.
Competition: 2011 Final project contest results and movie of drop, and class photo. John’s last words: “is that significant enough for you?”.

Exams

No exams. Note that the final project may take substantial time to develop and run experiments.
We will complete our final project presentations and contest before or on Thurs 12/15 3-5pm.

Text

Response Surface Methodology: Process and Product Optimization Using Designed Experiments (Wiley Series in Probability and Statistics)
Authors: Raymond H. Myers, Douglas C. Montgomery, Christine M. Anderson-Cook
Hardcover: 704 pages
Publisher: Wiley; 3 edition (January 14, 2009)
Language: English
ISBN-10: 0470174463
ISBN-13: 978-0470174463
Amazon: http://tinyurl.com/3vsc749

Course Objectives

At the end of this course, students should be able to:
1.  Understand fundamental concepts of matching experimental designs with analysis models.
2.  Recognize types of experimental designs and analysis models.
3.  Perform and interpret a proper response surface analysis.

Pre-design experiment guide sheet: pdf doc

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