By James D. White Jr
.
Plackett-Burman Design of Experiments
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Statistics developed in the early 20th
century
Tool to help improve yields in farming
Many types of experiments/techniques
Design of experiments when and who?
Designs of Experiments by Plackett and
Burman
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Were first written in 1946
R. L.. Plackett
J. P. Burman
Matrix design in structure
Improve quality control process
How does it help Improve the quality
control Process?
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Upper and lower level limits of a variables
Finds influencing factors
Helps with efficient estimating of process
Helps to improve the overall quality of the
product
Improving Quality of Product
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Experimental procedures require a
structured approach
Reliable results
Minimal wastage of time and money
Experimental design
Statistical principles
Limited number of experiments
Improving Quality of Product (continued)
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Optimize a process
Define which variables need most
control
Maintain the repeatability of a
process
A mathematical model of the process
Predict results of changed variables
Benefits of Knowing expected Results
when variables changed
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Variables on system can be enhanced
Design feasibility
Product robustness
Allows intelligent decision making
Which variable to change in a system?
Changing Variables In A System
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Modifying one variable is ineffective
Interactions cause unforeseen problems
Study Effects so intelligent decisions can
be made
Orthogonal array
Plackett-Burman Design
Plackett-Burman Experiments
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Two level fractional factorials
Efficient estimations
Interactions between factors ignored
Used In Matrix Form
Plackett-Burman (continued)
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Columns represent factors
Specify level to set for factors
Rows contain process runs
post-processing of results
Plackett-Burman (continued)
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Start with Factors
More factors The better
Factors go across the top
labeled f1, f2, . . . . f7.
Plackett-Burman (continued)
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The number of runs will go down columns
Multiples of 4 but not power of 2
On the last run we will use all (-) signs
Possible design of Plackett-Burman
design looks like the following:
Matrix Pattern of 7 Factors
Row
r1
r2
r3
r4
r5
r6
r7
r8
f1
+
+
+
+
-
f2
+
+
+
+
-
f3
+
+
+
+
-
f4
+
+
+
+
-
f5
+
+
+
+
-
f6
+
+
+
+
-
f7
+
+
+
+
-
Matrix Explained
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( - ) will have lower limits per variable
( + ) will have upper limits per variable
r1 is test one
f1 is variable one
(r1,f1) positive upper limit
Matrix explained (continued)
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(r2,f2) negative lower limit
Fill in the rest of the matrix the same way
Lower limits from test go in ( - )
Upper limits from test go in ( + )
Matrix Explained (continued)
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Find Upper level and Lower level limit
L = ¼ ( r1 + r4 + r6 + r7)
- ¼ ( r2 + r3 + r5 + r8)
Variable f1, r1-r8 going down not across.
Now have upper and lower limits of f1
Matrix Explained (continued)
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Get Value of upper level limit and value of
lower level limit
Once we have the values of Lower level
limit and upper level limit we can then
find the mean of that variable.
What does all this mean?
Meaning behind the means
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Variables can be changed
Change 1 variable
We now have mathematical formula
Change numbers and see change to the
process
Very advantageous
How could this tool be used in your
organization?
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Can you see the benefits?
Where else could you see this working?
Would it work in your organization?
Examples
Working example
Example of matrix
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Lets use a 2 variable matrix
We will have 8 runs
Matrix will look like the following:
Example Matrix structure
Row
R1
R2
R3
R4
R5
R6
R7
r8
f1
+
+
+
+
-
f2
+
+
+
+
-
Example matrix (continued)
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We will have 8 runs for variable 1
We will have 8 runs for variable 2
For ease of example we will make up
some numbers
Matrix will look like following with
numbers in it:
Example matrix structure with values
Row
R1
R2
R3
R4
R5
R6
R7
r8
f1
3
2
2.2
3.1
2.3
2.9
2.8
2.0
f2
3.1
2.7
1.9
2.0
3.5
2.1
3.0
2.0
Finding upper and lower limits
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Formula: L = ¼ ( r1 + r4 + r6 + r7)
- ¼ ( r2 + r3 + r5 + r8)
F1-UL = 2.95, LL = -2.12
F2-UL = 2.0, LL = -2.52
Find the means.
Means of example matrix
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Mean of variable 1 is ( .415)
Mean of variable 2 is - ( .26)
Change 2 runs
New table is as follows:
Example matrix after change of run 2
and 5
Row
R1
R2
R3
R4
R5
R6
R7
r8
f1
3
4
2.2
3.1
3.5
2.9
2.8
2.0
f2
3.1
5
1.9
2.0
2.9
2.1
3.0
2.0
Means of variables after change in
original variable runs
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Change of r2 to ( 4 ) and ( 5)
Change of r5 to ( 3.5 ) and ( 2.9 )
f1: UL = 2.95, LL =2.92
New mean of variable 1 =( .06)
f2: UL = 2.55, LL = 2.95
New mean of variable 2 = - ( .185)
Means of variables after change: net
change
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Net change of variable 1 = ( .355)
Net change of variable 2 = ( .075)
We can predict what changes will be
without any changes in process at this
time
Conclusion to Plackett and Burman
designs
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Change 1 to as many as N variables
Changes in variables are beneficial to
calculate
Not totally conclusive
Conclusion to Plackett and Burman
Designs
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Several programs available for help
Some that are available are as follows:
Minitab
S-plus
MINU
Calculators
Good luck in you future of quality
management
References cited page
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Draper N.R., “Plackett Burman Designs”,
Encyclopedia of Statistical Sciences
Volume 6, Ed Johnson Kotz, 9 volumes;
Wiley, 1982-1988
Trutna Ledi, “Process Improvements”,
Engineering Statistics Handbook, Ed.
Caroll Croarkin; No Date,
http://www.itl.nist.gov/div898/handbook/
index.htm