The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch.

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The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs Developed by Don Edwards, John Grego and James Lynch Center for Reliability and Quality Sciences Department of Statistics University of South Carolina 803-777-7800

Part I. Full Factorial Designs Introduction Analysis Tools Example Violin Exercise 2k Designs

How many combinations of factor levels are there? 24 Designs Introduction Suppose the effects of four factors, each having two levels, are to be investigated. How many combinations of factor levels are there? With 16 runs, one per each treatment combination, we can estimate: four main effects - (A,B,C,D) six two-way interactions - (AB,AC,AD,BC,BD,CD) four three-way interactions - (ABC,ABD,ACD,BCD) one four-way interaction (ABCD). 15 effects = 2^4 - 1

24 Designs Analysis Tools - Design Matrix No cube plot for now.

24 Designs Analysis Tools - Design Matrix Signs Table

24 Designs Analysis Tools - Signs Table Effects are divided by 8

24 Designs Analysis Tools - Fifteen Effects Paper

Response: Computer throughput (kbytes/sec), (large y’s are desirable) 24 Designs Example 4* Response: Computer throughput (kbytes/sec), (large y’s are desirable) Factors: A, B, C and D were various performance tuning parameters such as number of buffers size of unix inode tables for file handling *Data courtesy of Greg Dobbins

24 Designs Example 4 - Experimental Report Form

24 Designs Example 4 - Signs Table U-Do-It Fill Out the Signs Table to Estimate the Factor Effects If enough people are in class, we stop here and have each class member compute an effect, share effects then sort them. Think about a scale if using plotting paper, then plot effects.

24 Designs Example 4 - Completed Signs Table Try to sort effects here by hand

24 Designs Example 4 - Effects Normal Probability Plot Factors A and C Stand Out Choose Hi Settings of Both A and C since the response is throughput The large negative effects are on the WRONG side of the line—they are smaller than expected. We may have an issue with normality here. It’s hard to know how to treat the third and fourth largest positive effects.

24 Designs Example 4 - EMR at A=Hi, C=Hi

24 Designs Examples 2 and 4 Discussion Examples 2 (from Lecture 6.2) and 4 are Related Original Data Was In Tenths The Numbers were Rounded Off for Ease of Calculation Example 2 Half Fraction (24-1, 8 Runs) of the Data in Example 4. The Runs in Example 4 when ABCD=1 were the runs used in Example 2. Skip ahead to next slide to quickly show data table.

24 Designs Examples 2 and 4 Runs

24 Designs Example 2 and 4 - Effects Normal Probability Plots Factor A Still Stands Out The (Hidden) Replication in the Additional Runs Teased Out A Significant Effect Due to Factor C.