9,902 research outputs found
J2 optimality and Multi-level Minimum Aberration Criteria in fractional factorial design
The desirable properties of fractional factorial design: Balance and orthogonal; was examined for near balance and near orthogonal using the balance coefficient and J2 optimality criteria respectively. Efficient orthogonal arrays with three factors having two, three and four levels were constructed with balance and orthogonal property for lowest common multiples of runs. The two forms of balance coefficient were used for classifying the designs into two and multi level minimum aberration criteria were used to determine designs with lesser aberration. It was observed that designs constructed using the maximum form of balance coefficient has the lesser aberration in both the generalized minimum aberration and minimum moment aberration criteria. The J2 – optimality criterion reveals that the higher the run of a design, the lesser it’s optimality value. Keywords: Balance Coefficient, fractional factorial, Generalized Minimum Aberration (GMA), J2 optimality and Minimum Moment Aberration (MMA).
Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statistics
We give an expository review of applications of computational algebraic
statistics to design and analysis of fractional factorial experiments based on
our recent works. For the purpose of design, the techniques of Gr\"obner bases
and indicator functions allow us to treat fractional factorial designs without
distinction between regular designs and non-regular designs. For the purpose of
analysis of data from fractional factorial designs, the techniques of Markov
bases allow us to handle discrete observations. Thus the approach of
computational algebraic statistics greatly enlarges the scope of fractional
factorial designs.Comment: 16 page
Uniform fractional factorial designs
The minimum aberration criterion has been frequently used in the selection of
fractional factorial designs with nominal factors. For designs with
quantitative factors, however, level permutation of factors could alter their
geometrical structures and statistical properties. In this paper uniformity is
used to further distinguish fractional factorial designs, besides the minimum
aberration criterion. We show that minimum aberration designs have low
discrepancies on average. An efficient method for constructing uniform minimum
aberration designs is proposed and optimal designs with 27 and 81 runs are
obtained for practical use. These designs have good uniformity and are
effective for studying quantitative factors.Comment: Published in at http://dx.doi.org/10.1214/12-AOS987 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Design of Experiments for Screening
The aim of this paper is to review methods of designing screening
experiments, ranging from designs originally developed for physical experiments
to those especially tailored to experiments on numerical models. The strengths
and weaknesses of the various designs for screening variables in numerical
models are discussed. First, classes of factorial designs for experiments to
estimate main effects and interactions through a linear statistical model are
described, specifically regular and nonregular fractional factorial designs,
supersaturated designs and systematic fractional replicate designs. Generic
issues of aliasing, bias and cancellation of factorial effects are discussed.
Second, group screening experiments are considered including factorial group
screening and sequential bifurcation. Third, random sampling plans are
discussed including Latin hypercube sampling and sampling plans to estimate
elementary effects. Fourth, a variety of modelling methods commonly employed
with screening designs are briefly described. Finally, a novel study
demonstrates six screening methods on two frequently-used exemplars, and their
performances are compared
Aberration in qualitative multilevel designs
Generalized Word Length Pattern (GWLP) is an important and widely-used tool
for comparing fractional factorial designs. We consider qualitative factors,
and we code their levels using the roots of the unity. We write the GWLP of a
fraction using the polynomial indicator function, whose
coefficients encode many properties of the fraction. We show that the
coefficient of a simple or interaction term can be written using the counts of
its levels. This apparently simple remark leads to major consequence, including
a convolution formula for the counts. We also show that the mean aberration of
a term over the permutation of its levels provides a connection with the
variance of the level counts. Moreover, using mean aberrations for symmetric
designs with prime, we derive a new formula for computing the GWLP of
. It is computationally easy, does not use complex numbers and
also provides a clear way to interpret the GWLP. As case studies, we consider
non-isomorphic orthogonal arrays that have the same GWLP. The different
distributions of the mean aberrations suggest that they could be used as a
further tool to discriminate between fractions.Comment: 16 pages, 1 figur
Indicator function and complex coding for mixed fractional factorial designs
In a general fractional factorial design, the -levels of a factor are
coded by the -th roots of the unity. This device allows a full
generalization to mixed-level designs of the theory of the polynomial indicator
function which has already been introduced for two level designs by Fontana and
the Authors (2000). the properties of orthogonal arrays and regular fractions
are discussed
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