Singular factorial designs resulting from missing pairs of design points.

*(English)*Zbl 0642.62048In industry, experiments are often conducted sequentially due to equipment limitations dictating that only one or two simultaneous runs may be made. In this situation, early termination of the experiment results in missing points, leading to a loss in efficiency or, worse, to a singular subdesign with nonestimable model parameters. We investigate the specific problem of singularity when two points are lost from a factorial design based on n two-level factors. The method is based on the inner products of the coordinate vectors of the omitted design points and leads to some results on the nonexistence of fractional factorial designs.

##### Keywords:

factor level change; design resolution; defining contrast subgroup; missing points; problem of singularity; inner products; omitted design points; nonexistence of fractional factorial designs
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\textit{L. M. Moore}, J. Stat. Plann. Inference 19, No. 3, 325--340 (1988; Zbl 0642.62048)

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