Plackett-Burman Design of Plackett-Burman Design of Experiments Experiments 1. 1. Statistics developed in the Statistics developed in the early 20 early 20 th th century century 2. 2. Tool to help improve yields in Tool to help improve yields in farming farming 3. 3. Many types of Many types of experiments/techniques experiments/techniques 4. 4. Design of experiments when and Design of experiments when and who? who? By James D. White Jr By James D. White Jr . .
By James D. White Jr. Plackett-Burman Design of Experiments. Statistics developed in the early 20 th 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. - PowerPoint PPT Presentation
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Plackett-Burman Design of Plackett-Burman Design of ExperimentsExperiments
1.1. Statistics developed in the early Statistics developed in the early 2020thth century century
2.2. Tool to help improve yields in Tool to help improve yields in farmingfarming
3.3. Many types of Many types of experiments/techniques experiments/techniques
4.4. Design of experiments when and Design of experiments when and who?who?
By James D. White JrBy James D. White Jr..
Designs of Experiments by Designs of Experiments by Plackett and BurmanPlackett and Burman
1.1. Were first written in 1946Were first written in 1946
2.2. R. L.. PlackettR. L.. Plackett
3.3. J. P. BurmanJ. P. Burman
4.4. Matrix design in structureMatrix design in structure
5.5. Improve quality control processImprove quality control process
How does it help Improve the How does it help Improve the quality control Process?quality control Process?
1.1. Upper and lower level limits of a Upper and lower level limits of a variables variables
1.1. Get Value of upper level limit and Get Value of upper level limit and value of lower level limitvalue of lower level limit
2.2. Once we have the values of Once we have the values of Lower level limit and upper level Lower level limit and upper level limit we can then find the mean limit we can then find the mean of that variable.of that variable.
3.3. What does all this mean?What does all this mean?
Meaning behind the meansMeaning behind the means
1.1. Variables can be changedVariables can be changed
2.2. Change 1 variableChange 1 variable
3.3. We now have mathematical We now have mathematical formulaformula
4.4. Change numbers and see change Change numbers and see change to the processto the process
5.5. Very advantageousVery advantageous
How could this tool be used in How could this tool be used in your organization?your organization?
1.1. Can you see the benefits?Can you see the benefits?
2.2. Where else could you see this Where else could you see this working?working?
3.3. Would it work in your Would it work in your organization?organization?
4.4. ExamplesExamples
5.5. Working exampleWorking example
Example of matrixExample of matrix
1.1. Lets use a 2 variable matrixLets use a 2 variable matrix
2.2. We will have 8 runsWe will have 8 runs
3.3. Matrix will look like the following:Matrix will look like the following:
Example Matrix structureExample Matrix structure
RowRow f1f1 f2f2
R1R1 ++ ++
R2R2 -- ++
R3R3 -- --
R4R4 ++ --
R5R5 -- ++
R6R6 ++ --
R7R7 ++ ++
r8r8 -- --
Example matrix (continued)Example matrix (continued)
1.1. We will have 8 runs for variable 1We will have 8 runs for variable 1
2.2. We will have 8 runs for variable 2We will have 8 runs for variable 2
3.3. For ease of example we will make For ease of example we will make up some numbersup some numbers
4.4. Matrix will look like following with Matrix will look like following with numbers in it:numbers in it:
Example matrix structure with Example matrix structure with valuesvalues
RowRow f1f1 f2f2
R1R1 33 3.13.1
R2R2 22 2.72.7
R3R3 2.22.2 1.91.9
R4R4 3.13.1 2.02.0
R5R5 2.32.3 3.53.5
R6R6 2.92.9 2.12.1
R7R7 2.82.8 3.03.0
r8r8 2.02.0 2.02.0
Finding upper and lower limitsFinding upper and lower limits
1.1. Mean of variable 1 is ( .415)Mean of variable 1 is ( .415)
2.2. Mean of variable 2 is - ( .26)Mean of variable 2 is - ( .26)
3.3. Change 2 runs Change 2 runs
4.4. New table is as follows:New table is as follows:
Example matrix after change of Example matrix after change of run 2 and 5run 2 and 5
RowRow f1f1 f2f2
R1R1 33 3.13.1
R2R2 44 55
R3R3 2.22.2 1.91.9
R4R4 3.13.1 2.02.0
R5R5 3.53.5 2.92.9
R6R6 2.92.9 2.12.1
R7R7 2.82.8 3.03.0
r8r8 2.02.0 2.02.0
Means of variables after change Means of variables after change in original variable runsin original variable runs
1.1. Change of r2 to ( 4 ) and ( 5) Change of r2 to ( 4 ) and ( 5)
2.2. Change of r5 to ( 3.5 ) and ( 2.9 ) Change of r5 to ( 3.5 ) and ( 2.9 )
3.3. f1: UL = 2.95, LL =2.92f1: UL = 2.95, LL =2.92
4.4. New mean of variable 1 =( .06)New mean of variable 1 =( .06)
5.5. f2: UL = 2.55, LL = 2.95f2: UL = 2.55, LL = 2.95
6.6. New mean of variable 2 = - New mean of variable 2 = - ( .185)( .185)
Means of variables after change: Means of variables after change: net changenet change
1.1. Net change of variable 1 = ( .355)Net change of variable 1 = ( .355)
2.2. Net change of variable 2 = ( .075)Net change of variable 2 = ( .075)
3.3. We can predict what changes will We can predict what changes will be without any changes in be without any changes in process at this timeprocess at this time
Conclusion to Plackett and Conclusion to Plackett and Burman designsBurman designs
1.1. Change 1 to as many as N Change 1 to as many as N variables variables
2.2. Changes in variables Changes in variables are are beneficial to calculate beneficial to calculate
3.3. Not totally conclusive Not totally conclusive
Conclusion to Plackett and Conclusion to Plackett and Burman DesignsBurman Designs
1.1. Several programs available for helpSeveral programs available for help2.2. Some that are available are as Some that are available are as
follows:follows:3.3. MinitabMinitab4.4. S-plusS-plus5.5. MINUMINU6.6. Calculators Calculators 7.7. Good luck in you future of quality Good luck in you future of quality
managementmanagement
References cited pageReferences cited page
1.1. Draper N.R., “Plackett Burman Draper N.R., “Plackett Burman Designs”, Designs”, Encyclopedia of Statistical Encyclopedia of Statistical Sciences Volume 6, Sciences Volume 6, Ed Johnson Ed Johnson Kotz, 9 volumes; Wiley, 1982-1988Kotz, 9 volumes; Wiley, 1982-1988