RESULTS ON NON-ORTHOGONAL INCOMPLETE FACTORIAL DESIGNS
ROCKETDYNE CANOGA PARK CA
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The report consists of three distinct but related papers. The first is concerned with methods for constructing designs to meet realistic requirements on the number of runs and with criteria for selecting a design from a number of alternatives. Examples of various construction techniques are illustrated and designs are given which were constructed for actual experiments. Two specific numerical criteria are developed, and a convenient computer routine for evaluating them is described. The second paper discusses designs of even resolution. It is shown that the smallest resolution 4 designs for n factors at two levels must contain at least 2n runs, and that foldover designs are available with 2n runs. It is conjectured that the only minimal resolution 4 designs are foldover designs. The case of resolution 6 designs is also discussed. The third paper gives the variance bounds for estimates of main effects using one-at-a-time designs, and characterizes those designs which achieve the lower bounds. Situations in which runs are conducted a block at a time rather than singly are treated and it is shown that inclusion of interaction terms in the model improves the main-effect estimates of factors involved in the interactions.
- Statistics and Probability