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Theory of Orthogonal Designs |
This method of pruning is not perfect; it may prune a branch of the search tree that would have resulted in a success. In mathematical terms, candidate sets C_{i} are not necessarily isomorphic because they have the same size. You can use the NOCHECK option in the PROC FACTEX statement to turn off the pruning. With the NOCHECK option, the FACTEX procedure searches the entire tree of feasible confounding rules; and if given enough time, will find a design if one exists. The default argument for the TIME= option on the PROC FACTEX statement limits the search time to one minute.
On the other hand, you should recognize how rarely the NOCHECK option is needed to produce a design with a given resolution. For example, consider all possible blocked and unblocked two-level designs with minimum resolution for 50 or fewer factors and 128 or fewer runs. Of the 849 different designs, the NOCHECK option is required in only five cases. The five designs for which the NOCHECK option is required are listed in Table 16.1. Note that all of these are block designs, most for many factors and relatively small blocks.
Table 16.1: Designs Requiring the NOCHECK Option
Number of | Number of | Block | |
Factors | Runs | Size | Resolution |
5 | 16 | 2 | 4 |
21 | 32 | 4 | 3 |
22 | 32 | 4 | 3 |
23 | 32 | 4 | 3 |
39 | 64 | 4 | 3 |
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