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DESIGN OF EXPERIMENTS

Learn the Analyst’s purposes of understanding, explanation, prediction, and control in the design of experiments. Explore preferred predictors, points of departure, options like regression methods and Taguchi methods, and sound experimental procedures.

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DESIGN OF EXPERIMENTS

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  1. DESIGN OF EXPERIMENTS M. Piczak November 2005

  2. THE ANALYST’S PURPOSES • UNDERSTANDING (a command of general cause and effect relationships associated with a particular phenomenon) • EXPLANATION (application of selected relationships to a particular observation) • PREDICTION (extending knowledge of relationships to a future event) • CONTROL (intervening with the intent of either stimulating or preventing a particular event)

  3. PREFERRED PREDICTORS • GYPSIES • BOOKIES • TAROT CARDS • PALM READERS • FARMER’S ALMANAC • HOROSCOPE • FORTUNE COOKIES • EQUATIONS

  4. POINT PREDICTION VERSUS GENERAL STATEMENTS

  5. NARROWING THE KNOWLEDGE GAP

  6. THE DOE OBJECTIVE: • To establish a causal link between selected independent variables X’s and particular dependent Y variables • To isolate or disentangle the independent effect being exerted on a response variable

  7. POINT OF DEPARTURE • Ho: That there exists no relationship between the X and Y variable (assumes that the value of the coefficient for Xi = 0) • Ha: That there exists a relationship between the X and Y variable The challenge is to disprove Ho and thus, accept Ha

  8. OPTIONS PRESENT THEMSELVES • REGRESSION METHODS • TAGUCHI METHODS • SHAININ METHODS • 6 SIGMA METHODS • CLASSIC DESIGN OF EXPERIMENTS

  9. SOUND EXPERIMENTAL PROCEDURE • Start with a uniformity, regularity or anomaly worthy of examination (See ‘What is Worth Studying’) • Establish the research questions • Undertake a literature review to identify other key explanatory variables (See ‘Weird Predictors’) • Explicate the relevant theory for each X variable as it relates to Y, a priori • Establish the measures for X and Y • Choose an experimental design using Minitab • Execute the experiment • Gather the data • Analyze the data • Draw conclusions • Repeat as necessary to cumulate knowledge

  10. LEARNING WITH AN EXAMPLE F = M * A Where: F = Force M = Mass A = Acceleration

  11. SETTING UP THE DATA F = M * A

  12. ADDING THE Y DATA F = M * A

  13. CALCULATING COEFFICIENTS F = M * A

  14. STAT, DOE, FACTORIAL, CREATE FACTORIAL DESIGN

  15. WITH PERFECT RESULTS

  16. STAT, DOE, FACTORIAL, ANALYZE FACTORIAL DESIGN

  17. WILL REGRESSION GIVE THE SAME RESULTS? CODED DATA

  18. RUNNING UNCODED ALL X’s

  19. RUNNING F = M * A ALONE

  20. THE THEORY Thus, the actual model:

  21. TRANSFORMING THE CODED MODEL INTO ACTUAL Ma & Mc   or Ma = 7.5 + 2.5Mc Therefore

  22. RELATIONSHIP BETWEEN CODED & UNCODED VALUES

  23. SIMILARLY FOR ACCELERATION or Aa = 150 + 50 Ac Therefore

  24. SUBSTITUTING TERMS F = M * A

  25. “TA DA”…F = M * A

  26. BUT THE ANSWER WAS THERE THE WHOLE TIME…WHERE IS IT?

  27. OTHER RESOURCES • http://www.airacad.com/PaperDOE.aspx • http://www.statease.com/pubs/popcorn.pdf • http://thequalityportal.com/q_know02.htm • http://www.hq.nasa.gov/office/hqlibrary/ppm/ppm35.htm • http://www.isixsigma.com/tt/doe/

  28. DESIGN OF EXPERIMENTS M. Piczak November 2005 THE END

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