The Normal Symmetrical Partial Factor Design Under The MEC Criterion

Factorial designs have been widely applied in many fields. When the number of factors is large, and we cannot conduct the experiment with all combinations of the levels of the factors due to time, money and the other reasons, we often use fractional factorial designs.Blocking is one of fundamental principles of experimental design. When the experimental units are not, homogencous, we often use the blocked designs. The construction of optimal designs is important in the investigation of experimental designs.This article studies regular fractions of symetrical factorial A criterion of model robustness, called estimation capacity. is introduced and explored. Maximun estimation ca-pacity(MEC) aims at selecting a design that retains full information on the main dffects.and as much information as possible on the two-factor interactions in the sense of entertaining the maximun possible model diversity under the assumption of absence of interactions involving three or more factors. As the MEC criterion requires too much, this paper presents a relaxed version of MEC (Partial maximum estimation capacity. PMEC) criterion. The relationship between the minimun aberration (MA) criterion and MEC and PMEC criteria is explored.It is proved that, when k=1, the MA 2n-k design is the MEC design, and when k=2,3,the MA 2n-k design is also the PMEC design. For small k, it gives the construction methods of the optimal two-level fractional factorial designs 2n-k under the criterion of MEC or the criterion of PMEC. The article also investigates the construction methods of the optimal blocked design 2n : 2s under the criterion of MEC or PMEC. It proves that, the MEC 2n:2s design and the MA 2n : 2s design are the same. The construction methods of the optimal blocked design 2n-k : 2s with small k and s are given.