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

2.2. Finds influencing factors Finds influencing factors

3.3. Helps with efficient estimating of Helps with efficient estimating of processprocess

4.4. Helps to improve the overall Helps to improve the overall quality of the productquality of the product

Improving Quality of ProductImproving Quality of Product

1.1. Experimental procedures require a Experimental procedures require a structured approach structured approach

2.2. Reliable resultsReliable results

3.3. Minimal wastage of time and Minimal wastage of time and moneymoney

4.4. Experimental designExperimental design

5.5. Statistical principles Statistical principles

6.6. Limited number of experiments Limited number of experiments

ImprovingImproving Quality of Product Quality of Product (continued)(continued)

1.1. Optimize a process Optimize a process 2.2. Define which variables need most Define which variables need most

control control 3.3. Maintain the repeatability of a Maintain the repeatability of a

process process 4.4. A mathematical model of the A mathematical model of the

process process 5.5. Predict results of changed variables Predict results of changed variables

Benefits of Knowing expected Benefits of Knowing expected Results when variables changedResults when variables changed

1.1. Variables on system Variables on system can be can be enhancedenhanced

2.2. Design feasibilityDesign feasibility

3.3. Product robustness Product robustness

4.4. Allows intelligent decision makingAllows intelligent decision making

5.5. Which variable to change in a Which variable to change in a system?system?

Changing Variables In A SystemChanging Variables In A System

1.1. Modifying one variable is Modifying one variable is ineffectiveineffective

2.2. Interactions cause unforeseen Interactions cause unforeseen problemsproblems

3.3. Study Effects so intelligent Study Effects so intelligent decisions can be madedecisions can be made

4.4. Orthogonal arrayOrthogonal array

5.5. Plackett-Burman DesignPlackett-Burman Design

Plackett-Burman ExperimentsPlackett-Burman Experiments

1.1. Two level fractional factorials Two level fractional factorials

2.2. Efficient estimations Efficient estimations

3.3. Interactions between factors Interactions between factors ignoredignored

4.4. Used In Matrix FormUsed In Matrix Form

Plackett-Burman (continued)Plackett-Burman (continued)

1.1. Columns represent factors Columns represent factors

2.2. Specify level to set for factors Specify level to set for factors

3.3. Rows contain process runsRows contain process runs

4.4. post-processing of resultspost-processing of results

Plackett-Burman (continued)Plackett-Burman (continued)

1.1. Start with Factors Start with Factors

2.2. More factors The betterMore factors The better

3.3. Factors go across the topFactors go across the top

4.4. labeled f1, f2, . . . . f7. labeled f1, f2, . . . . f7.

Plackett-Burman (continued)Plackett-Burman (continued)

1.1. The number of runs will go down The number of runs will go down columnscolumns

2.2. Multiples of 4 but not power of 2 Multiples of 4 but not power of 2

3.3. On the last run we will use all (-) On the last run we will use all (-) signssigns

4.4. Possible design of Plackett-Possible design of Plackett-Burman design looks like the Burman design looks like the following:following:

Matrix Pattern of 7 FactorsMatrix Pattern of 7 Factors

RowRow f1f1 f2f2 f3f3 f4f4 f5f5 f6f6 f7f7

r1r1 ++ ++ ++ -- ++ -- --

r2r2 -- ++ ++ ++ -- ++ --

r3r3 -- -- ++ ++ ++ -- ++

r4r4 ++ -- -- ++ ++ ++ --

r5r5 -- ++ -- -- ++ ++ ++

r6r6 ++ -- ++ -- -- ++ ++

r7r7 ++ ++ -- ++ -- -- ++

r8r8 -- -- -- -- -- -- --

Matrix ExplainedMatrix Explained

1.1. ( - ) will have lower limits per ( - ) will have lower limits per variablevariable

2.2. ( + ) will have upper limits per ( + ) will have upper limits per variablevariable

3.3. r1 is test one r1 is test one

4.4. f1 is variable onef1 is variable one

5.5. (r1,f1) positive upper limit(r1,f1) positive upper limit

Matrix explained (continued)Matrix explained (continued)

1.1. (r2,f2) negative lower limit(r2,f2) negative lower limit

2.2. Fill in the rest of the matrix the Fill in the rest of the matrix the same waysame way

3.3. Lower limits from test go in ( - )Lower limits from test go in ( - )

4.4. Upper limits from test go in ( + )Upper limits from test go in ( + )

Matrix Explained (continued)Matrix Explained (continued)

1.1. Find Upper level and Lower level Find Upper level and Lower level limitlimit

2.2. L = ¼ ( r1 + r4 + r6 + r7) L = ¼ ( r1 + r4 + r6 + r7)

3.3. - ¼ ( r2 + r3 + r5 + r8) - ¼ ( r2 + r3 + r5 + r8)

4.4. Variable f1, r1-r8 going down not Variable f1, r1-r8 going down not across. across.

5.5. Now have upper and lower limits of Now have upper and lower limits of f1f1

Matrix Explained (continued)Matrix Explained (continued)

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. Formula: L = ¼ ( r1 + r4 + r6 + r7)Formula: L = ¼ ( r1 + r4 + r6 + r7)2.2. - ¼ ( r2 + r3 + - ¼ ( r2 + r3 +

r5 + r8)r5 + r8)3.3. F1-UL = 2.95, LL = -2.12F1-UL = 2.95, LL = -2.124.4. F2-UL = 2.0, LL = -2.52F2-UL = 2.0, LL = -2.525.5. Find the means. Find the means.

Means of example matrixMeans of example matrix

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

2.2. Trutna Ledi, “Process Trutna Ledi, “Process Improvements”, Improvements”, Engineering Engineering Statistics Handbook, Statistics Handbook, Ed. Caroll Ed. Caroll Croarkin; No Date, Croarkin; No Date, http://www.itl.nist.gov/div898/handbook/index.htm