The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs

1. The Essentials of 2-Level Design of ExperimentsPart I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James LynchCenter for Reliability and Quality SciencesDepartment of StatisticsUniversity of South Carolina803-777-7800

2. Part I: The Essentials of Full Factorial Designs • Some Motivation and Background • Two Important Advantages of Factorial Experiments • The Essentials of 2-Cubed Designs • Full Factorial Designs

3. I.1 Some MotivationArno PenziasChief Scientist and VP for Research, Bell Labs & Nobel Laureate-Physics “Teaching Statistics to Engineers,” Science Editorial, June 2 1989 • Statistical Tools Are Needed In Industry • Competitive Position Demands It • Optimizing Complex Technological Manufacturing Processes Requires It

4. I.1 Some Motivation • Leaders In Quality • Use Statistics At All Process Stages For Quality and Optimization Purposes • Provide The Necessary Statistical Training To Do This

5. I.1 Some MotivationQS9000 • QS9000 required that “The supplier shall demonstrate knowledge in Design of Experiments (DOE) and use it as appropriate.”

6. I.1 Some MotivationExamples of DOE Applications • NCR has used factorial designs in a variety of situations, e.g., to analyze computer performance and to compare different soldering methods. • Sara Lee Hosiery Division has used simple designs in a number of settings. Several have resulted in considerable annual savings.

7. I.1 Some MotivationExamples of DOE Applications • Ohio Brass has conducted several fractional factorial designs which have had significant impact. One study resulted in an annual savings of $25K by modifying an existing process and avoided a capital investment of a 1/4 to 1/2 million dollars in new equipment. Another enabled them to reduce the dimensions of two key components which resulted in annual savings of $50K.

8. I.1 Some MotivationExamples of DOE Applications • Michelin has used designs to determine maintenance programs for some of their machinery.

9. I.1 BackgroundWhy Should You Use DOE? • Intelligent Decisions Should Be Based On "Informed Observation And Directed Experimentation" (George Box) • It is consistent with the Scientific Method which is fundamental to the quality management philosophy (The Deming-Shewhart PDSA Cycle) • DOE is a formalism that forces you to organize your thoughts (so you don't do things haphazardly)

10. I.1 BackgroundWhy Should You Use DOE? • DOE Concentrates Your Efforts • Screening designs aid in identifying the vital/critical factors that may affect the (process) response of interest • More refined design techniques determine the factor levels that optimize the response

11. I.1 BackgroundWhy Should You Use DOE? • DOE Concentrates Your Efforts • DOE helps you to understand how factors affect the process. This knowledge helps to choose factor settings that are cost effective but don’t compromise quality (constrained optimization).

12. I.1 BackgroundQuality Management Philosophy • Some Tenets Related to These Components • All processes have variation • Different types of variation • e.g., common cause system verses special causes being present • Management needs predictable/stable processes to make decisions (process needs to be in control, i.e., a common cause variation system)

13. I.1 BackgroundQuality Management Philosophy • Implications for DOE • The smaller the effects you are trying to detect relative to the background variation, the more replication you need or a different design (blocking) • Data from an out-of-control process is suspect

14. I.1 BackgroundContrasting SPC and DOE • Statistical Process Control (SPC) • SPC is used to determine if a process is in control • An Out-of-Control process that is brought into control is not process improvement (Juran)

15. I.1 BackgroundContrasting SPC and DOE • Design of Experiments (DOE) • A methodology useful for determining • what factors may affect a response • what factor settings are feasible • SPC Lets You Listen to the Process;DOE Allows You to Converse With It William Hunter

16. I.1 BackgroundExperimentation • Experiment • A series of trials or tests which produce quantifiable outcomes. • Quantifiable Outcome • Some Outcome Measurement of Interest • “Response Variable” (y)

17. I.1 BackgroundExamples of Responses • Yield • Viscosity • Computer Performance • Breaking Strength of Fiber • Smoothness of Polyurethane Sheets • Bowing of a Molding • Chain Length in Polymer • Number of Flaws

18. I.1 BackgroundResponses- Bowing of a Molding • Three Moldings • Top - Most Severe Bowing • Bottom - Flat, No Bowing

19. I.1 BackgroundResponses- Bowing of a Molding True versus Substitute Quality Characteristics • The Displacement D • Substitute Quality Characteristic for Bowing • Measurable

20. I.1 BackgroundFactors • Experimental (Variable) Conditions That May Affect the Response. • A. Flow rate of a raw material • B. Process temperature • C. Presence/Absence of a Catalyst • D. Raw Material Supplier (e.g. 1,2, or 3)

21. I.1 BackgroundFactors • Factors May Be • Continuous (A and B Above) • Discrete (C and D Above)

22. I.1 BackgroundFirst Motivation To Experiment • To “Improve” The Response..... • Optimize average response • Minimize variability in response • Minimize susceptibility to uncontrollable “noise” factors

23. I.1 BackgroundBest Motivation • To “Understand” The Response! (George Box) • Levels of Understanding • Which? • How? • Why?

24. I.1 BackgroundLevels of UnderstandingAn Example - Yellowfin Tuna Growth • Traditional Theoretical Growth Models Allow For Only One Point of Inflection(Two Growth Stages)

25. I.1 BackgroundLevels of Understanding : “How” StageAn Example - Yellowfin Tuna Growth • Lowess Fit Suggests • Two Points of Inflection • Rethink Theory

26. I.1 BackgroundLevels of Understanding: “How” StageAn Example - Yellowfin Tuna Growth • More Pronounced In The Atlantic Ocean Yellowfin Tuna

27. I.1 BackgroundLevels of Understanding: “Why” Stage An Example - Yellowfin Tuna Growth