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July, 1976 Balanced Fractional $2^m$ Factorial Designs of Even Resolution Obtained from Balanced Arrays of Strength $2l$ with Index $\mu_l = 0$
Teruhiro Shirakura
Ann. Statist. 4(4): 723-735 (July, 1976). DOI: 10.1214/aos/1176343544

Abstract

Consider a balanced array $T$ of strength 2$l,$ size $N, m$ constraints and index set $\{\mu_0, \mu_1,\cdots, \mu_{2l}\}$ with $\mu_l = 0$. Under some conditions $T$ yields a design of even resolution ($2l$, say) with $N$ assemblies such that all the effects involving up to $(l - 1)$-factor interactions are estimable provided $(l + 1)$-factor and higher order interactions are assumed negligible and that the covariance matrix of their estimates is invariant under any permutation of $m$ factors. The alias structure of the effects of $l$-factor interactions is explicitly given. Such an array $T$ is called an $S$-type balanced fractional $2^m$ factorial design of resolution $2l$. Necessary conditions for the existence of the design $T$ are given. For any given $N$, there are in general a large number of possible $S$-type balanced fractional $2^m$ factorial designs of resolution $2l$. Finally a criterion for comparing these designs is given.

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Teruhiro Shirakura. "Balanced Fractional $2^m$ Factorial Designs of Even Resolution Obtained from Balanced Arrays of Strength $2l$ with Index $\mu_l = 0$." Ann. Statist. 4 (4) 723 - 735, July, 1976. https://doi.org/10.1214/aos/1176343544

Information

Published: July, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0337.62054
MathSciNet: MR418366
Digital Object Identifier: 10.1214/aos/1176343544

Subjects:
Primary: 62K15
Secondary: 05B30

Keywords: association algebra , balanced arrays , balanced designs , contrasts , Covariance matrix , even resolution , optimality

Rights: Copyright © 1976 Institute of Mathematical Statistics

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Vol.4 • No. 4 • July, 1976
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