Premium
Adding more observations to saturated D‐optimal resolution III two‐level factorial designs
Author(s) -
Hedayat A. S.,
Zhu Haiyuan
Publication year - 2002
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.10026
Subject(s) - mathematics , class (philosophy) , combinatorics , factorial experiment , fractional factorial design , set (abstract data type) , value (mathematics) , factorial , resolution (logic) , upper and lower bounds , matrix (chemical analysis) , variance (accounting) , discrete mathematics , statistics , computer science , artificial intelligence , mathematical analysis , materials science , accounting , business , composite material , programming language
We consider the class of saturated main effect plans for the 2 k factorial. With these saturated designs, the overall mean and all main effects can be unbiasedly estimated provided that there are no interactions. However, there is no way to estimate the error variance with such designs. Because of this and other reasons, we like to add some additional runs to the set of ( k +1) runs in the D‐optimal design in this class. Our goals here are: (1) to search for s additional runs so that the resulting design based on ( k + s +1) runs yields a D‐optimal design in the class of augmented designs; (2) to classify all the runs into equivalent classes so that the runs in the same equivalent class give us the same value of the determinant of the information matrix. This allows us to trade runs for runs if this becomes necessary; (3) to obtain upper bounds for determinant of the information matrices of augmented designs. In this article we shall address these approaches and present some new results. © 2002 Wiley Periodicals, Inc. J Combin Designs 11: 51–77, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jcd.10026