# A note on uniformity and orthogonality

Chang Xing Ma, Kai Tai Fang, Dennis K.J. Lin

Research output: Contribution to journalArticle

26 Citations (Scopus)

### Abstract

Fang et al. (Technometrics 42 (2000) 237) proposed a united approach for searching orthogonal fractional factorial designs. They conjecture an important "equivalence theorem" between the uniformity of experimental points over the domain and the design orthogonality. They showed numerically that uniformity of experimental points over the domain can imply design orthogonality and conjecture that every orthogonal design can be obtained by minimizing some measure of uniformity. This paper shows that their conjecture is only true in some special cases.

Original language English (US) 323-334 12 Journal of Statistical Planning and Inference 113 1 https://doi.org/10.1016/S0378-3758(01)00293-2 Published - Apr 1 2003

### Fingerprint

Orthogonality
Uniformity
Orthogonal Design
Equivalence Theorem
Fractional Factorial Design
Imply
Design

### All Science Journal Classification (ASJC) codes

• Statistics and Probability
• Statistics, Probability and Uncertainty
• Applied Mathematics

### Cite this

Ma, Chang Xing ; Fang, Kai Tai ; Lin, Dennis K.J. / A note on uniformity and orthogonality. In: Journal of Statistical Planning and Inference. 2003 ; Vol. 113, No. 1. pp. 323-334.
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A note on uniformity and orthogonality. / Ma, Chang Xing; Fang, Kai Tai; Lin, Dennis K.J.

In: Journal of Statistical Planning and Inference, Vol. 113, No. 1, 01.04.2003, p. 323-334.

Research output: Contribution to journalArticle

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