Premium
NECESSARY AND SUFFICIENT CONDITION FOR A BALANCED ARRAY OF STRENGTH 21 TO BE A BALANCED FRACTIONAL 2 FACTORIAL DESIGN OF RESOLUTION 2l
Author(s) -
Shirakura Teruhiro
Publication year - 1980
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1980.tb01155.x
Subject(s) - fractional factorial design , mathematics , resolution (logic) , permutation (music) , orthogonal array , factorial experiment , factorial , covariance matrix , invariant (physics) , covariance , matrix (chemical analysis) , factor (programming language) , property (philosophy) , combinatorics , statistics , computer science , mathematical analysis , taguchi methods , artificial intelligence , physics , philosophy , epistemology , acoustics , mathematical physics , materials science , composite material , programming language
Summary A necessary and sufficient condition for a balanced array of strength 2l to be a balanced fractional 2 m factorial design of resolution 2l is given. This design has the property that the main effects, two‐factor interactions,.and (l‐1)‐factor interactions are estimable ignoring the (l + 1)‐factor and higher order interactions, and that the covariance matrix of their estimates is invariant under any permutation of m factors. The above condition includes sufficient conditions given in earlier works of Shirakura (1976b, 1977).