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
- Mathematics
- 2020
Results for Two-Level Designs with General Minimum Lower-Order Confounding
- Computer ScienceTheScientificWorldJournal
- 2015
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
- Mathematics
- 2016
On constructing general minimum lower order confounding two-level block designs
- Mathematics
- 2017
ABSTRACT In practice, to reduce systematic variation and increase precision of effect estimation, a practical design strategy is then to partition the experimental units into homogeneous groups,…
Some results on constructing two-level block designs with general minimum lower order confounding
- Mathematics
- 2018
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…
A theory on constructing blocked two-level designs with general minimum lower order confounding
- Mathematics
- 2016
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…
A theory on constructing blocked two-level designs with general minimum lower order confounding
- MathematicsFrontiers of Mathematics in China
- 2015
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…
Lower-order confounding information of inverse Yates-order two-level designs
- MathematicsCommunications in Statistics - Theory and Methods
- 2019
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
- Materials ScienceMetrika
- 2022
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
- MathematicsJ. Syst. Sci. Complex.
- 2018
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.
References
SHOWING 1-10 OF 11 REFERENCES
A Complementary Design Theory for Doubling
- Mathematics
- 2008
Chen and Cheng (2006a) discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for 9N/32<= n<= 5N/16, all minimum aberration designs with N runs and…
Characterization of general minimum lower order confounding via complementary sets
- Mathematics
- 2009
With reference to regular fractions of general s-level factorials, we consider the design criterion of general minimum lower order confounding (GMC) that aims, in an elaborate manner, at keeping the…
Minimum Aberration 2k-p Designs
- Mathematics
- 1980
Fractional factorial designs-especially the twolevel designs-are useful in a variety of experimental situations, for example, (i) screening studies in which only a subset of the variables is expected…
Doubling and projection: A method of constructing two-level designs of resolution IV
- Mathematics
- 2006
Given a two-level regular fractional factorial design of resolution IV, the method of doubling produces another design of resolution IV which doubles both the run size and the number of factors of…
A Modern Theory Of Factorial Designs
- Mathematics
- 2006
The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives,…
2n-l designs with weak minimum aberration
- Mathematics
- 1996
Since not all 2 n-l fractional factorial designs with maximum resolution are equally good, Fries and Hunter introduced the minimum aberration criterion for selecting good 2 n-l fractional factorial…
Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs
- Mathematics
- 1996
A general result is obtained that relates the word-length pattern of a 2 n-k design to that of its complementary design. By applying this result and using group isomorphism, we are able to…
A graph-aided method for planning two-level experiments when certain interactions are important
- Mathematics
- 1992
In planning a fractional factorial experiment prior knowledge may suggest that some interactions are potentially important and should therefore be estimated free of the main effects. In this article,…
Some theory for constructing minimum aberration fractional factorial designs
- Mathematics
- 2003
Minimum aberration is the most established criterion for selecting a regular fractional factorial design of maximum resolution. Minimum aberration designs for n runs and ns2
Minimum Aberration 2 k–p Designs
- Mathematics, Physics
- 1980
For studying k variables in N runs, all 2 k–p designs of maximum resolution are not equally good. In this paper the concept of aberration is proposed as a way of selecting the best designs from those…