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**Blocked regular fractional factorial designs with maximum estimation capacity.**
*(English)*
Zbl 1041.62064

Ann. Stat. 29, No. 2, 530-548 (2001); correction ibid. 30, No. 3, 925-926 (2002).

Summary: The problem of constructing optimal blocked regular fractional factorial designs is considered. The concept of minimum aberration due to A. Fries and W. G. Hunter [Technometrics 22, 601–608 (1980; Zbl 0453.62063)] is a well-accepted criterion for selecting good unblocked fractional factorial designs. C. S. Cheng, D.M. Steinberg and D. X. Sun [J. R. Stat. Soc., Ser. B 61, 85–93 (1999; Zbl 0913.62072)] showed that a minimum aberration design of resolution three or higher maximizes the number of two-factor interactions which are not aliases of main effects and also tends to distribute these interactions over the alias sets very uniformly.

We extend this to construct block designs in which (i) no main effect is aliased with any other main effect not confounded with blocks, (ii) the number of two-factor interactions that are neither aliased with main effects nor confounded with blocks is as large as possible and (iii) these interactions are distributed over the alias sets as uniformly as possible.

Such designs perform well under the criterion of maximum estimation capacity, a criterion of model robustness which has a direct statistical meaning. Some general results on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach.

We extend this to construct block designs in which (i) no main effect is aliased with any other main effect not confounded with blocks, (ii) the number of two-factor interactions that are neither aliased with main effects nor confounded with blocks is as large as possible and (iii) these interactions are distributed over the alias sets as uniformly as possible.

Such designs perform well under the criterion of maximum estimation capacity, a criterion of model robustness which has a direct statistical meaning. Some general results on the construction of blocked regular fractional factorial designs with maximum estimation capacity are obtained by using a finite projective geometric approach.

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