1. The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina 803-777-7800

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

3. I.1 Some Motivation Arno Penzias Chief 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 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 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 Motivation QS9000 QS9000 required that “The supplier shall demonstrate knowledge in Design of Experiments (DOE) and use it as appropriate.” QS9000 required that “The supplier shall demonstrate knowledge in Design of Experiments (DOE) and use it as appropriate.”

6. I.1 Some Motivation Examples 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. 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. Sara Lee Hosiery Division has used simple designs in a number of settings. Several have resulted in considerable annual savings.

7. I.1 Some Motivation Examples 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. 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 Motivation Examples of DOE Applications Michelin has used designs to determine maintenance programs for some of their machinery. Michelin has used designs to determine maintenance programs for some of their machinery.

9. I.1 Background Why Should You Use DOE? Intelligent Decisions Should Be Based On "Informed Observation And Directed Experimentation" (George Box) 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 Background Why Should You Use DOE? DOE Concentrates Your Efforts 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 Background Why Should You Use DOE? DOE Concentrates Your Efforts 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 Background Quality Management Philosophy Some Tenets Related to These Components 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 Background Quality Management Philosophy Implications for DOE 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 Background Contrasting SPC and DOE Statistical Process Control (SPC) 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 Background Contrasting SPC and DOE Design of Experiments (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 SPC Lets You Listen to the Process; DOE Allows You to Converse With It William Hunter

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

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

18. I.1 Background Responses- Bowing of a Molding Three Moldings Three Moldings –Top - Most Severe Bowing –Bottom - Flat, No Bowing Three Moldings Three Moldings –Top - Most Severe Bowing –Bottom - Flat, No Bowing

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

20. I.1 Background Factors Experimental (Variable) Conditions That May Affect the Response. 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 Background Factors Factors May Be Factors May Be –Continuous (A and B Above) –Discrete (C and D Above)

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

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

24. I.1 Background Levels of Understanding An Example - Yellowfin Tuna Growth Traditional Theoretical Growth Models Allow For Only One Point of Inflection (Two Growth Stages) Traditional Theoretical Growth Models Allow For Only One Point of Inflection (Two Growth Stages)

25. I.1 Background Levels of Understanding : “How” Stage An Example - Yellowfin Tuna Growth Lowess Fit Suggests Lowess Fit Suggests –Two Points of Inflection –Rethink Theory Lowess Fit Suggests Lowess Fit Suggests –Two Points of Inflection –Rethink Theory

26. I.1 Background Levels of Understanding: “How” Stage An Example - Yellowfin Tuna Growth More Pronounced In The Atlantic Ocean Yellowfin Tuna More Pronounced In The Atlantic Ocean Yellowfin Tuna

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