A new series of main effects plus one plan for 2m factorial experiments with m=4λ±1 and 2m runs

Esmailzadeh, Nabaz; Talebi, Hooshang; Momihara, Koji; Jimbo, Masakazu

doi:10.1016/j.jspi.2010.11.008

Cited by 4 publications

(7 citation statements)

References 7 publications

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“…The resulting designs and those supplied by Esmailzadeh et al (2011) completely fill the existing gap in search designs with respect to the number of factors. These results are new in the sense of providing single array search designs in contrast to all the two-array MEP.1 plans constructed previously.…”

Section: Introductionmentioning

confidence: 95%

“…Let us take (a 1 , a 2 ,…, a h ) to be a treatment combination corresponding to any h factors numbered by the set {1, 2, 3,…, m} where factor levels a i (i = 1, 2,…, h) are either 0 or 1. Following Esmailzadeh et al (2011) we also denote the number of runs in T 1 which have a given treatment combination (a 1 , a 2 ,…, a h ) by N (a 1 ,a 2 ,…,a h )…”

Section: Model and Notationmentioning

confidence: 99%

“…Details and the history of these designs can be found in Ghosh, Shirakura & Srivastava (2007). Recently, Esmailzadeh et al (2011) provided a search design for odd m in 2 m factorial experiments. In all of the literature cited above, the authors have considered a main effect plan and then characterized conditions on a follow-up design so that the augmented design becomes an MEP.k plan.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting designs were search designs for m = 4 − 1, 2 with 2m + 1 runs. Esmailzadeh et al (2011) used the same MEP but employed a partially balanced incomplete block design (PBIBD) so as to specify a suitable follow-up design. Their investigation improved the resulting MEP.1 plans with respect to the number of runs (N = 2m) in addition to adding flexibility in the number of factors involved in the experiment, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…This gap was reduced to 4 by Ghosh & Talebi (1993) who constructed MEP.1 plans for m = 4 − 1 ( 2). Esmailzadeh et al (2011) succeeded in filling the gap by giving MEP.1 plans for all odd m which reduced the gap from 4 to 2. They suggested deleting a column from the corresponding given MEP.1 plans so as to obtain the MEP.1 plans for even m. This was done at the cost of diminished structure of the augmented arrays search design and hence the possibility of losing some of the optimal properties of the effect estimates.…”

Section: Introductionmentioning

confidence: 99%

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A series of single array 2^mfactorial search designs for evenm

Talebi

Jalali

2014

Aust. N. Z. J. Stat.

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By means of a search design one is able to search for and estimate a small set of nonzero elements from the set of higher order factorial interactions in addition to estimating the lower order factorial effects. One may be interested in estimating the general mean and main effects, in addition to searching for and estimating a non-negligible effect in the set of 2-and 3-factor interactions, assuming 4-and higher-order interactions are all zero. Such a search design is called a 'main effect plus one plan' and is denoted by MEP.1. Construction of such a plan, for 2 m factorial experiments, has been considered and developed by several authors and leads to MEP.1 plans for an odd number m of factors. These designs are generally determined by two arrays, one specifying a main effect plan and the other specifying a follow-up. In this paper we develop the construction of search designs for an even number of factors m, m = 6. The new series of MEP.1 plans is a set of single array designs with a well structured form. Such a structure allows for flexibility in arriving at an appropriate design with optimum properties for search and estimation.

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Section: Introductionmentioning

confidence: 95%

Section: Model and Notationmentioning

confidence: 99%