# Plackett-Burman Design of Experiments 1. Statistics developed in the early 20 th century 2. Tool to help improve yields in farming 3. Many types of experiments/techniques.

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Plackett-Burman Design of Experiments 1. Statistics developed in the early 20 th century 2. Tool to help improve yields in farming 3. Many types of experiments/techniques 4. Design of experiments when and who? By James D. White Jr.

Designs of Experiments by Plackett and Burman 1. Were first written in 1946 2. R. L.. Plackett 3. J. P. Burman 4. Matrix design in structure 5. Improve quality control process

How does it help Improve the quality control Process? 1. Upper and lower level limits of a variables 2. Finds influencing factors 3. Helps with efficient estimating of process 4. Helps to improve the overall quality of the product

Improving Quality of Product 1. Experimental procedures require a structured approach 2. Reliable results 3. Minimal wastage of time and money 4. Experimental design 5. Statistical principles 6. Limited number of experiments

Improving Quality of Product (continued) 1. Optimize a process 2. Define which variables need most control 3. Maintain the repeatability of a process 4. A mathematical model of the process 5. Predict results of changed variables

Benefits of Knowing expected Results when variables changed 1. Variables on system can be enhanced 2. Design feasibility 3. Product robustness 4. Allows intelligent decision making 5. Which variable to change in a system?

Changing Variables In A System 1. Modifying one variable is ineffective 2. Interactions cause unforeseen problems 3. Study Effects so intelligent decisions can be made 4. Orthogonal array 5. Plackett-Burman Design

Plackett-Burman Experiments 1. Two level fractional factorials 2. Efficient estimations 3. Interactions between factors ignored 4. Used In Matrix Form

Plackett-Burman (continued) 1. Columns represent factors 2. Specify level to set for factors 3. Rows contain process runs 4. post-processing of results

Plackett-Burman (continued) 1. Start with Factors 2. More factors The better 3. Factors go across the top 4. labeled f1, f2,.... f7.

Plackett-Burman (continued) 1. The number of runs will go down columns 2. Multiples of 4 but not power of 2 3. On the last run we will use all (-) signs 4. Possible design of Plackett-Burman design looks like the following:

Matrix Pattern of 7 Factors Rowf1f2f3f4f5f6f7 r1+++-+-- r2-+++-+- r3--+++-+ r4+--+++- r5-+--+++ r6+-+--++ r7++-+--+ r8-------

Matrix Explained 1. ( - ) will have lower limits per variable 2. ( + ) will have upper limits per variable 3. r1 is test one 4. f1 is variable one 5. (r1,f1) positive upper limit

Matrix explained (continued) 1. (r2,f2) negative lower limit 2. Fill in the rest of the matrix the same way 3. Lower limits from test go in ( - ) 4. Upper limits from test go in ( + )

Matrix Explained (continued) 1. Find Upper level and Lower level limit 2. L = ¼ ( r1 + r4 + r6 + r7) 3. - ¼ ( r2 + r3 + r5 + r8) 4. Variable f1, r1-r8 going down not across. 5. Now have upper and lower limits of f1

Matrix Explained (continued) 1. Get Value of upper level limit and value of lower level limit 2. Once we have the values of Lower level limit and upper level limit we can then find the mean of that variable. 3. What does all this mean?

Meaning behind the means 1. Variables can be changed 2. Change 1 variable 3. We now have mathematical formula 4. Change numbers and see change to the process 5. Very advantageous

How could this tool be used in your organization? 1. Can you see the benefits? 2. Where else could you see this working? 3. Would it work in your organization? 4. Examples 5. Working example

Example of matrix 1. Lets use a 2 variable matrix 2. We will have 8 runs 3. Matrix will look like the following:

Example Matrix structure Rowf1f2 R1++ R2-+ R3-- R4+- R5-+ R6+- R7++ r8--

Example matrix (continued) 1. We will have 8 runs for variable 1 2. We will have 8 runs for variable 2 3. For ease of example we will make up some numbers 4. Matrix will look like following with numbers in it:

Example matrix structure with values Rowf1f2 R133.1 R222.7 R32.21.9 R43.12.0 R52.33.5 R62.92.1 R72.83.0 r82.02.0

Finding upper and lower limits 1. Formula: L = ¼ ( r1 + r4 + r6 + r7) 2. - ¼ ( r2 + r3 + r5 + r8) 3. F1-UL = 2.95, LL = -2.12 4. F2-UL = 2.0, LL = -2.52 5. Find the means.

Means of example matrix 1. Mean of variable 1 is (.415) 2. Mean of variable 2 is - (.26) 3. Change 2 runs 4. New table is as follows:

Example matrix after change of run 2 and 5 Rowf1f2 R133.1 R245 R32.21.9 R43.12.0 R53.52.9 R62.92.1 R72.83.0 r82.02.0

Means of variables after change in original variable runs 1. Change of r2 to ( 4 ) and ( 5) 2. Change of r5 to ( 3.5 ) and ( 2.9 ) 3. f1: UL = 2.95, LL =2.92 4. New mean of variable 1 =(.06) 5. f2: UL = 2.55, LL = 2.95 6. New mean of variable 2 = - (.185)

Means of variables after change: net change 1. Net change of variable 1 = (.355) 2. Net change of variable 2 = (.075) 3. We can predict what changes will be without any changes in process at this time

Conclusion to Plackett and Burman designs 1. Change 1 to as many as N variables 2. Changes in variables are beneficial to calculate 3. Not totally conclusive

Conclusion to Plackett and Burman Designs 1. Several programs available for help 2. Some that are available are as follows: 3. Minitab 4. S-plus 5. MINU 6. Calculators 7. Good luck in you future of quality management

References cited page

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