# SOME THEORY FOR CONSTRUCTING GENERAL MINIMUM LOWER ORDER CONFOUNDING DESIGNS

@article{Chen2011SOMETF, title={SOME THEORY FOR CONSTRUCTING GENERAL MINIMUM LOWER ORDER CONFOUNDING DESIGNS}, author={Jie Chen and Min-Qian Liu}, journal={Statistica Sinica}, year={2011}, volume={21} }

General minimum lower order confounding (GMC) is a newly proposed design criterion that aims at keeping the lower order effects unaliased with one another to the extent possible. This paper shows that for 5N/16 < n ≤ N/2, 9N/32 < n ≤ 5N/16, and 17N/64 < n ≤ 9N/32, all GMC designs with N runs and n two-level factors are projections of maximal designs with N/2, 5N/16, and 9N/32 factors, respectively. Furthermore, it provides immediate approaches to construct- ing these GMC designs from the…

## 20 Citations

### Construction of some s-level regular designs with general minimum lower-order confounding

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The interior principles to calculate the leading elements 1 # C 2 and 2 # C2 in the AENP are shown and their mathematical formulations are obtained for every GMC 2n−m design with N = 2 n−m.

### A note on the construction of blocked two-level designs with general minimum lower order confounding

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### On constructing general minimum lower order confounding two-level block designs

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ABSTRACT Block designs are widely used in experimental situations where the experimental units are heterogeneous. The blocked general minimum lower order confounding (B-GMC) criterion is suitable for…

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Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when…

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Completely random allocation of the treatment combinations to the experimental units is appropriate only if the experimental units are homogeneous. Such homogeneity may not always be guaranteed when…

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Abstract Based on the effect hierarchy principle, a good design should minimize the confounding among the lower-order effects. Thus, it is important to obtain the confounding information of effects…

### Lower-order confounding information of inverse Yates-order designs with three levels

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Li et al. (Comm Statist Theory Methods 49: 924–941, 2020) introduced the concept of inverse Yates-order (IYO) designs, and obtained most of two-level IYO designs have general minimum lower-order…

### On Construction of Optimal Two-Level Designs with Multi Block Variables

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This paper proposes a systematic theory on constructing some B2-GMC designs for the first time and reveals the pros and cons of the designs according to the construction method.

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