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Small run size design for model identification in 3 m factorial experiments
Author(s) -
Labbaf Fariba Z.,
Talebi Hooshang
Publication year - 2020
Publication title -
stat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.61
H-Index - 18
ISSN - 2049-1573
DOI - 10.1002/sta4.299
Subject(s) - fractional factorial design , factorial experiment , alias , main effect , mathematics , statistics , factorial , design of experiments , interaction , variance (accounting) , plackett–burman design , identification (biology) , selection (genetic algorithm) , computer science , artificial intelligence , data mining , mathematical analysis , botany , accounting , response surface methodology , biology , business
An active interaction in a main effect plan may cause biased estimation of the parameters in an analysis of variance (ANOVA) model. A fractional factorial design (FFD) with higher order resolution can resolve the alias problem, however, with a considerable number of runs. Alternatively, a search design (SD), the so‐called main effect plus k plan (MEP. k ), with much less number of runs than FFD, is able to search for k possible active interactions and estimate them in addition to estimating the main effects. However, the existing MEP. k 's for 3 m factorial experiments are either proposed for a large m (e.g. m ≥ 13) or have a large number of runs. In this paper, we proposed an irregular design for 3 m factorial experiments, which is able to identify the active two‐factor interactions and estimate them along with estimating the general mean and main effects for 3 ≤ m ≤ 14. The obtained design has fewer runs than the previous designs; meanwhile, it is also comparable and competitive in the discrimination and estimation performances with them. By simulation studies, it is shown that the proposed design does well in model identification and variable selection.