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

Shengli Zhao; Dennis K.J. Lin; Pengfei Li

doi:10.1016/j.jspi.2015.12.007

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

Shengli Zhao, Dennis K.J. Lin, Pengfei Li

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Abstract

Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2^n-m:2^r design, where 2^n-m:2^r denotes a two-level regular blocked design with N=2^n-m runs, n treatment factors and 2^r blocks. This paper gives the first construction method of B-GMC 2^n-m:2^r designs with 5N/16+1≤n≤N/2. The results indicate that under isomorphism, with suitable choice of the blocking factors, each B-GMC blocked design has a common specific structure. Examples are included to illustrate the developed theory.

Original language	English (US)
Pages (from-to)	16-22
Number of pages	7
Journal	Journal of Statistical Planning and Inference
Volume	172
DOIs	https://doi.org/10.1016/j.jspi.2015.12.007
State	Published - May 1 2016

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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title = "A note on the construction of blocked two-level designs with general minimum lower order confounding",

abstract = "Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2n-m:2r design, where 2n-m:2r denotes a two-level regular blocked design with N=2n-m runs, n treatment factors and 2r blocks. This paper gives the first construction method of B-GMC 2n-m:2r designs with 5N/16+1≤n≤N/2. The results indicate that under isomorphism, with suitable choice of the blocking factors, each B-GMC blocked design has a common specific structure. Examples are included to illustrate the developed theory.",

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AU - Zhao, Shengli

AU - Lin, Dennis K.J.

AU - Li, Pengfei

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N2 - Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2n-m:2r design, where 2n-m:2r denotes a two-level regular blocked design with N=2n-m runs, n treatment factors and 2r blocks. This paper gives the first construction method of B-GMC 2n-m:2r designs with 5N/16+1≤n≤N/2. The results indicate that under isomorphism, with suitable choice of the blocking factors, each B-GMC blocked design has a common specific structure. Examples are included to illustrate the developed theory.

AB - Blocked designs are useful in experiments. The general minimum lower order confounding (GMC) is an elaborate criterion which was proposed for selecting optimal fractional factorial designs. Zhang and Mukerjee (2009b) extended the GMC criterion to the B-GMC criterion for selecting a 2n-m:2r design, where 2n-m:2r denotes a two-level regular blocked design with N=2n-m runs, n treatment factors and 2r blocks. This paper gives the first construction method of B-GMC 2n-m:2r designs with 5N/16+1≤n≤N/2. The results indicate that under isomorphism, with suitable choice of the blocking factors, each B-GMC blocked design has a common specific structure. Examples are included to illustrate the developed theory.

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