1. The Essentials of 2-Level Design of Experiments Part I: The Essentials of Full Factorial Designs 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

2. Part I. Full Factorial Designs 2 4 Designs 2 4 Designs –Introduction –Analysis Tools –Example –Violin Exercise 2 k Designs 2 k Designs

3. 2 4 Designs Introduction Suppose the effects of four factors, each having two levels, are to be investigated. Suppose the effects of four factors, each having two levels, are to be investigated. How many combinations of factor levels are there? 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).

4. 2 4 Designs Analysis Tools - Design Matrix

5. 2 4 Designs Analysis Tools - Design Matrix Signs Table

6. 2 4 Designs Analysis Tools - Signs Table

7. 2 4 Designs Analysis Tools - Fifteen Effects Paper

8. 2 4 Designs Example 4 * Response: Computer throughput (kbytes/sec), (large y’s are desirable) Response: Computer throughput (kbytes/sec), (large y’s are desirable) Factors: A, B, C and D were various performance tuning parameters such as 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

9. 2 4 Designs Example 4 - Experimental Report Form

10. 2 4 Designs Example 4 - Signs Table U-Do-It Fill Out the Signs Table to Estimate the Factor Effects Fill Out the Signs Table to Estimate the Factor Effects

11. 2 4 Designs Example 4 - Completed Signs Table

12. 2 4 Designs Example 4 - Effects Normal Probability Plot Factors A and C Stand Out Factors A and C Stand Out Choose Hi Settings of Both A and C since the response is throughput Choose Hi Settings of Both A and C since the response is throughput Factors A and C Stand Out Factors A and C Stand Out Choose Hi Settings of Both A and C since the response is throughput Choose Hi Settings of Both A and C since the response is throughput

13. 2 4 Designs Example 4 - EMR at A=Hi, C=Hi EMR = 69.125 +(5.5 + 2.25)/2 = 73 EMR = 69.125 +(5.5 + 2.25)/2 = 73

14. 2 4 Designs Examples 2 and 4 Discussion Examples 2 (from Lecture 6.2) and 4 are Related 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 Example 2 –Half Fraction (2 4-1, 8 Runs) of the Data in Example 4. –The Runs in Example 4 when ABCD=1 were the runs used in Example 2.

15. 2 4 Designs Examples 2 and 4 Discussion

16. 2 4 Designs Example 2 and 4 - Effects Normal Probability Plots Factor A Still Stands Out Factor A Still Stands Out The (Hidden) Replication in the Additional Runs Teased Out A Significant Effect Due to Factor C. The (Hidden) Replication in the Additional Runs Teased Out A Significant Effect Due to Factor C.