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
  Lynch Center 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 Motivation QS9000

• 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 dont
  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 ProcessDOE Allows
  You to Converse With It
  William Hunter

16
I.1 Background Experimentation

• Experiment
• A series of trials or tests which produce
  quantifiable outcomes.
• Quantifiable Outcome
• Some Outcome Measurement of Interest
• Response Variable (y)

17
I.1 Background Examples 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 Background Responses- Bowing of a Molding

• 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
• Substitute Quality Characteristic for Bowing
• Measurable

20
I.1 Background Factors

• 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
• Continuous (A and B Above)
• Discrete (C and D Above)

22
I.1 Background First Motivation To Experiment

• To Improve The Response.....
• Optimize average response
• Minimize variability in response
• Minimize susceptibility to uncontrollable noise
  factors

23
I.1 Background Best Motivation

• To Understand The Response! (George Box)
• Levels of Understanding
• Which?
• How?
• Why?

24
I.1 Background Levels of UnderstandingAn
Example - Yellowfin Tuna Growth

• Traditional Theoretical Growth Models Allow For
  Only One Point of Inflection(Two Growth Stages)

25
I.1 Background Levels of Understanding How
StageAn Example - Yellowfin Tuna Growth

• Lowess Fit Suggests
• Two Points of Inflection
• Rethink Theory

26
I.1 Background Levels of Understanding How
StageAn Example - Yellowfin Tuna Growth

• More Pronounced In The Atlantic Ocean Yellowfin
  Tuna

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