Record Details

Some Investigations on Minimum Aberration for Fractional Factorials

KrishiKosh

View Archive Info
 
 
Field Value
 
Title Some Investigations on Minimum Aberration for Fractional Factorials
Ph D
 
Creator Nitiprasad N. Jambhulkar
 
Contributor Krishan Lal
 
Subject ---
 
Description T-8406
Factorial experiments are widely used in agriculture and several other branches of science. Factorial experiments aim at exploring the effects of the individual factors and their inter-relationship as well. Factorial experiments are of two types, symmetric and asymmetric. When all the factors are at same level then the experiment is called symmetric, otherwise asymmetric. A factorial experiment, where each treatment combination is applied to one experimental unit, is called a complete factorial. However, quite often in practice, the total number of treatment combinations is too large to allow the use of a complete factorial unless the number of factors and the levels of the factors are too small. Factorial experiment with large number of treatment combinations, apart from being expensive and impracticable in most situations, may not be at all necessary if the interest is in estimating only lower order effects under the assumption of absence of higher order effects. Moreover, in planning big experiments non-experimental types of error may also creep in. These errors may be because of mishandling of the big experiment in the sense that the treatment labeling may be changed or plot number may be wrongly noted. Economy of space and material may be attained by observing the response only on a fraction of all possible treatment combinations. Thus, the experiment that includes only a fraction of the totality of all possible treatment combinations is called fractional factorial experiment. The technique of recovering useful information by observing only part of the complete factorial is known as fractional factorials. Fractional factorial experiments are of two types regular and irregular. When fractional factorials are obtained through defining contrasts it is called regular fractional factorial otherwise called irregular fractional factorial. In any factorial experiment, the experimenter is interested in estimating main effects and lower order interactions under the assumption that higher order interactions are negligible. Fractional factorial plans are characterized by different resolution plans. Box and Hunter (1961) and Webb (1968) have given different definitions of resolution plans. If two fractional factorial designs are of same resolution then Fries and Hunter (1980) has introduced the concept of minimum
aberration based on wordlength pattern to select the best design out of the two designs
with same resolution. The criterion based on wordlength pattern works only to regular
fractional factorial designs. Other criteria of minimum aberration that are applicable to
other experimental situations such as irregular fractional factorials have been given.
These minimum aberration criteria are Minimum G-aberration criterion (1999),
Minimum Moment Aberration criterion (2003), Moment Aberration Projection (2005)
criterion. In this thesis two level, multi-level and mixed level minimum aberration
fractional factorial plans have been constructed. Two level irregular minimum aberration
plans have been constructed of the type k
p
r
2
2




where ( 2 ) p r  is a prime number in 12,
20, 24, 28, 40, 48, 56, 80, 96, 112, 160, 224 runs. For r = 3 and p = 2, the minimum
aberration fractional factorial plans have been constructed for k = 4, 5, 6 and 7 in 12, 24,
48 and 96 runs respectively. For r = 3 and p = 3, the minimum aberration fractional
factorial plans have been constructed for k = 5, 6, 7 and 8 in 12, 24, 48 and 96 runs
respectively. For r = 5 and p = 3, the minimum aberration fractional factorial plans have
been constructed for k = 5, 6, 7 and 8 in 20, 40, 80 and 160 runs respectively. For r = 7
and p = 3, the minimum aberration fractional factorial plans have been constructed for
k = 5, 6, 7 and 8 in 28, 56, 112 and 224 runs respectively. Multilevel minimum aberration
fractional factorial plans have been constructed of the type k p s  where s is prime number.
For s = 5, the minimum aberration fractional factorial plans have been constructed in 125
runs for the value of k ranges from 4 to 15 and the value of p ranges from 1 to 12. For
s = 7, the minimum aberration fractional factorial plans have been constructed in 343
runs for the value of k ranges from 4 to 15 and the value of p ranges from 1 to 12. Mixed
level minimum aberration fractional factorial plans have been constructed of the type
m n 4 2 in 64 and 128 runs. n 4 2 1 minimum aberration fractional factorial plans have been
constructed for n = 6 to 10 in 128 runs. n 4 2 2 minimum aberration fractional factorial
plans have been constructed for n = 4 to 7 in 128 runs. Minimum aberration fractional
factorial plans have been constructed of the type n 4 2 3 for n = 1 to 4 in 64 runs and for
n = 2 to 6 in 128 runs. SAS code has been developed in SAS 9.2 for the construction of
above minimum aberration fractional factorial plans. Catalogues for the above designs
have also been prepared which will serve as a ready reckoner to the practicing statisticians and the experimenters. These designs are quite helpful to the experimenters when there is scarcity of the experimental resources and fractional factorial experiments have to be applied.
 
Date 2016-11-02T10:05:40Z
2016-11-02T10:05:40Z
2011
 
Type Thesis
 
Identifier http://krishikosh.egranth.ac.in/handle/1/83246
 
Format application/pdf
 
Publisher IARI, Indian Agricultural Statistics Research Institute