## Hiroshima Mathematical Journal

- Hiroshima Math. J.
- Volume 37, Number 1 (2007), 119-143.

### GA-optimal partially balanced fractional $2^{m_1+m_2}$ factorial designs of resolution ${R}(\{00,10,01\}|\Omega)$} with $2\leq m_1,m_2 \leq 4$

Shujie Lu, Eiji Taniguchi, Masahide Kuwada, and Yoshifumi Hyodo

#### Abstract

Under the assumption that the three-factor and higher-order interactions are negligible, we consider a partially balanced fractional $2^{m_1+m_2}$ factorial design derived from a simple partially balanced array such that the general mean, all the $m_1+m_2$ main effects, and some linear combinations of $\binom{m_1}{2}$ two-factor interactions, of the $\binom{m_2}{2}$ ones and of the $m_1m_2$ ones are estimable, where $2\leq m_k$ for $k=1,2$. This paper presents optimal designs with respect to the generalized A-optimality criterion when the number of assemblies is less than the number of non-negligible factorial effects, where $2\leq m_1, m_2 \leq 4$.

#### Article information

**Source**

Hiroshima Math. J., Volume 37, Number 1 (2007), 119-143.

**Dates**

First available in Project Euclid: 11 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.hmj/1176324099

**Digital Object Identifier**

doi:10.32917/hmj/1176324099

**Mathematical Reviews number (MathSciNet)**

MR2308528

**Zentralblatt MATH identifier**

1138.62043

**Subjects**

Primary: 62K05: Optimal designs

Secondary: 05B30: Other designs, configurations [See also 51E30]

**Keywords**

ETMDPB association algebra GA-optimality criterion parametric functions PBFF designs resolution SPBA

#### Citation

Lu, Shujie; Taniguchi, Eiji; Kuwada, Masahide; Hyodo, Yoshifumi. GA-optimal partially balanced fractional $2^{m_1+m_2}$ factorial designs of resolution ${R}(\{00,10,01\}|\Omega)$} with $2\leq m_1,m_2 \leq 4$. Hiroshima Math. J. 37 (2007), no. 1, 119--143. doi:10.32917/hmj/1176324099. https://projecteuclid.org/euclid.hmj/1176324099