Transcript Tabular and Graphical Methodology for 23 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
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

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
– Competitive Position Demands It
– Optimizing Complex Technological
Manufacturing Processes Requires It
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
I.1 Some Motivation
QS9000

QS9000 required that
“The supplier shall demonstrate
knowledge in Design of Experiments (DOE)
and use it as appropriate.”
I.1 Some Motivation
Examples of DOE Applications
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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.
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.
I.1 Some Motivation
Examples of DOE Applications

Michelin has used designs to determine
maintenance programs for some of their
machinery.
I.1 Background
Why 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)
I.1 Background
Why 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
I.1 Background
Why 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).
I.1 Background
Quality 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)
I.1 Background
Quality 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
I.1 Background
Contrasting 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)
I.1 Background
Contrasting 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
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)
I.1 Background
Examples of Responses

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Yield
Viscosity
Computer Performance
Breaking Strength of Fiber
Smoothness of Polyurethane Sheets
Bowing of a Molding
Chain Length in Polymer
Number of Flaws
I.1 Background
Responses- Bowing of a Molding

Three Moldings
– Top - Most Severe
Bowing
– Bottom - Flat, No
Bowing
I.1 Background
Responses- Bowing of a Molding
True versus Substitute Quality
Characteristics

The Displacement D
– Substitute Quality
Characteristic for
Bowing
– Measurable
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)
I.1 Background
Factors

Factors May Be
– Continuous (A and B Above)
– Discrete (C and D Above)
I.1 Background
First Motivation To Experiment
To “Improve” The Response.....
 Optimize average response
 Minimize variability in response
 Minimize susceptibility to uncontrollable
“noise” factors

I.1 Background
Best Motivation
To “Understand” The Response! (George
Box)
 Levels of Understanding

– Which?
– How?
– Why?
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)
Indian Ocean Yellowfin Tuna
Age versus Fork Leng th
120
110
100
90
Fork 80
Length 70
(cm) 60
50
40
30
0
500
A ge (days)
1000
I.1 Background
Levels of Understanding : “How” Stage
An Example - Yellowfin Tuna Growth

Lowess Fit Suggests
– Two Points of
Inflection
– Rethink Theory
Indian Ocean Yellowfin Tuna
Age versus Fork Leng th
120
110
100
90
Fork 80
Length 70
(cm)
60
50
40
30
0
500
A ge (days)
1000
I.1 Background
Levels of Understanding: “How” Stage
An Example - Yellowfin Tuna Growth

More
Pronounced In
The Atlantic
Ocean Yellowfin
Tuna
Atlantic Ocean Yellowfi n Tuna
Age versus Fork Leng th
110
100
90
Fork
Length
(cm)
80
70
60
50
400
500
600
700
A ge (days)
800
900
I.1 Background
Levels of Understanding: “Why” Stage
An Example - Yellowfin Tuna Growth
Atlantic Ocean Yellowfin Tuna
Age versus Fork Leng th
110
G onadal
Stage
100
90
Fork
Length
(c m)
80
70
Somatic
Stages
60
50
400
500
600
700
A ge (days )
800
900