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.3 The Essentials of 2-Cubed Designs

Methodology
– Cube Plots
– Estimating Main Effects
– Estimating Interactions (Interaction
Tables and Graphs)
Statistical Significance:
When is an Effect “Real”?
 An Example With Interactions
 A U-Do-It Case Study
 Replication


Rope Pull Exercise
U-Do-It Case Study
Ball Bearing Example*

Purpose of the Design
– Test (Under Accelerated Conditions) New Bearing Prototypes for Use
in a Specific Application for Which the Current Design’s Performance
Was “Unsatisfactory”.
– Response of Interest: y - Bearing Life (h).

Design Factors:
– Factor
A: Cage Design
B: Outer Ring Osculation
C: Inner Ring Heat Treatment.

Levels (Lo,Hi)
Current, New
Current, New
Current, New
The 8 Standard Runs of the 23 Design Were Randomly
Ordered, and Each Prototype Bearing Tested.
*Empirical Basis for this data was motivated by C. Hellstrand’s article “The necessity of modern
quality improvement and some experiences with implications in the manufacture of ball bearings
(1989, Philos. Trans. Royal Society London, A 327, 529-537)
U-Do-It Case Study
Ball Bearing Example - A Typical Ball Bearing
U-Do-It Case Study
Ball Bearing Example - Operator Report Form
Experimental
Run Order
1
2
3
4
5
6
7
8
Standard
Order Trial
Number
4
7
1
8
3
2
5
6
Cage
Design
A
new
current
current
new
current
new
current
new
Outer Ring
Osculation
B
new
new
current
new
new
current
current
current
Inner Ring Heat
Treatment
C
current
new
current
new
current
current
new
new
Bearing
Life (h)
Y
21
99
18
112
25
16
24
17
U-Do-It Case Study
Ball Bearing Example - Exercise Instructions

Exercise
– Put the results of the experiment in
standard order and enter the data into a
cube plot (in Minitab—see handout)
– Estimate the factor effects (in Minitab)
– Construct and interpret a normal
probability plot of the factor effects (in
Minitab)
U-Do-It Case Study
Ball Bearing Example - Exercise Instructions

Exercise
– Construct BC interaction graph in Minitab;
use table and graph to interpret BC
interaction
– Determine the factor settings that
maximize bearing life and estimate the
Mean Response (EMR) at these settings.
How close is your answer to the observed
mean response at your optimal settings?
– If you would like to do hand calculations,
blank signs tables, cube plots, etc. are
provided over the next several slides
U-Do-It Case Study
Ball Bearing Example - Signs Table
Main Effects
Actual
Run
Sum
Divisor
Effect
8
Interaction Effects
A
-1
1
-1
1
-1
1
-1
1
B
-1
-1
1
1
-1
-1
1
1
C
-1
-1
-1
-1
1
1
1
1
AB
1
-1
-1
1
1
-1
-1
1
AC
1
-1
1
-1
-1
1
-1
1
BC
1
1
-1
-1
-1
-1
1
1
ABC
-1
1
1
-1
1
-1
-1
1
4
4
4
4
4
4
4
U-Do-It Case Study
Ball Bearing Example - Cube Plot
+
B
+
C
_
_
_
A
+
U-Do-It Case Study
Ball Bearing Example - Seven Effects Paper
7 Effects Plot
7
6
5
4
3
2
1
Effects
U-Do-It Case Study
Ball Bearing Example - Interaction Table
1
1
2
2