A Sequential Approach of Estimating Two Factor Interactions
A Sequential Approach of Estimating Two Factor Interactions
Bin Zhou
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After deleting all repeated experimental runs the total number of runs is only 74 in the above 12 factor experiment. To find out how many runs are needed in the proposed procedures, we did the following simulation when ISM is known to be sparse. For n factors and different sparses, we generate 1, 000 ISM's by randomly placing p x 100% of ofF-diagnal entries non-zero. For n = 6, .... 20 and p = 25%, 50%, 75%, we cal- culated the average required experiment runs (without considering repeatc^i run...s). The results are listed in Table 3. In general if m interaction effects needed to be estimated, our procedure would require a little bit more than 2m nms. Table 3: The numbers of experimental runs needed in the sequential ap- proaches Factors P=-25% P=50% P=75% 6 11. 3 (1. 5(')) 21. 8 (2. 2) 32. 2 (1. 1) 7 17. 3 (1. 9) 29. 8 (2. 4) 46. 0 (2. 5) 8 23. Ti (2. 4) 41. 6 (2. 7) 65. 3 (9. 6) 9 29. 4 (2. 7) 51. 3 (3. 5) 78. 6 (7. 5) 10 34. 4 (2. 8) 63. 2 (4. 1) 91. 4 (4. 3) 11 40. 6 (3. 5) 76. 2 (5.
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