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Plackett-Burman Design of Experiments

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.

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Plackett-Burman Design of Experiments

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  1. By James D. White Jr. Plackett-Burman Design of Experiments • 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?

  2. Designs of Experiments by Plackett and Burman • Were first written in 1946 • R. L.. Plackett • J. P. Burman • Matrix design in structure • Improve quality control process

  3. How does it help Improve the quality control Process? • 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

  4. Improving Quality of Product • Experimental procedures require a structured approach • Reliable results • Minimal wastage of time and money • Experimental design • Statistical principles • Limited number of experiments

  5. ImprovingQuality of Product (continued) • 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

  6. Benefits of Knowing expected Results when variables changed • Variables on system can be enhanced • Design feasibility • Product robustness • Allows intelligent decision making • Which variable to change in a system?

  7. Changing Variables In A System • Modifying one variable is ineffective • Interactions cause unforeseen problems • Study Effects so intelligent decisions can be made • Orthogonal array • Plackett-Burman Design

  8. Plackett-Burman Experiments • Two level fractional factorials • Efficient estimations • Interactions between factors ignored • Used In Matrix Form

  9. Plackett-Burman (continued) • Columns represent factors • Specify level to set for factors • Rows contain process runs • post-processing of results

  10. Plackett-Burman (continued) • Start with Factors • More factors The better • Factors go across the top • labeled f1, f2, . . . . f7.

  11. Plackett-Burman (continued) • 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:

  12. Matrix Pattern of 7 Factors

  13. Matrix Explained • ( - ) 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

  14. Matrix explained (continued) • (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 ( + )

  15. Matrix Explained (continued) • 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

  16. Matrix Explained (continued) • 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?

  17. Meaning behind the means • Variables can be changed • Change 1 variable • We now have mathematical formula • Change numbers and see change to the process • Very advantageous

  18. How could this tool be used in your organization? • Can you see the benefits? • Where else could you see this working? • Would it work in your organization? • Examples • Working example

  19. Example of matrix • Lets use a 2 variable matrix • We will have 8 runs • Matrix will look like the following:

  20. Example Matrix structure

  21. Example matrix (continued) • 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:

  22. Example matrix structure with values

  23. Finding upper and lower limits • 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.

  24. Means of example matrix • Mean of variable 1 is ( .415) • Mean of variable 2 is - ( .26) • Change 2 runs • New table is as follows:

  25. Example matrix after change of run 2 and 5

  26. Means of variables after change in original variable runs • 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)

  27. Means of variables after change: net change • 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

  28. Conclusion to Plackett and Burman designs • Change 1 to as many as N variables • Changes in variables are beneficial to calculate • Not totally conclusive

  29. Conclusion to Plackett and Burman Designs • 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

  30. References cited page • 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

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