Semifoldover plans for three-level orthogonal arrays with quantitative factors
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Semifoldover plans for three-level orthogonal arrays with quantitative factors Wenlong Li1 · Bing Guo2 · Hengzhen Huang3 · Min-Qian Liu1 Received: 26 February 2020 / Revised: 25 August 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Although foldover designs can de-alias many effects, they involve at least twice the original number of runs. A semifoldover design, one kind of the partial foldover designs, is typically much more efficient since such a design adds only half of the new runs of a foldover design to the initial design. Semifoldover designs for two-level orthogonal arrays have been investigated in recent literatures. With the use of linearquadratic system, this paper considers semifoldover designs for three-level orthogonal arrays with quantitative factors. We examine when the linear effects can be de-aliased from their aliased two-factor interactions for regular and nonregular designs, and obtain some good properties via semifolding over on partial factors or all factors. Theoretical properties and some examples are provided to illustrate the usefulness of the proposed designs. Keywords Combined design · Generalized wordlength pattern · Linear-quadratic system · Semifoldover design
1 Introduction Two-level factorial designs are often used to screen factors and determine which factorial effects are important. However, three-level designs are sometimes more appropriate for factor screening and interaction detection (Wu and Hamada 2009; Xu et al. 2004). The number of runs of the full 3k factorial design exponentially increases as the number of factors k increases. For this reason, fractional factorial designs, i.e. fractions of full 3k factorial designs, are often more desirable in practical applications.
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Min-Qian Liu [email protected]
1
School of Statistics and Data Science, LPMC & KLMDASR, Nankai University, Tianjin 300071, China
2
College of Mathematics, Sichuan University, Chengdu 610065, China
3
College of Mathematics and Statistics, Guangxi Normal University, Guilin 541004, China
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W. Li et al.
One consequence of employing fractional factorial designs is the aliasing of factorial effects. Traditionally, foldover is a popular de-aliasing technique that may de-alias factorial effects by adding 1 and 2 (modulo 3) to one or more factors of the initial design (Ai et al. 2008; Ou et al. 2015). The initial design together with the newly added runs as a whole is called the foldover design. Nevertheless the foldover technique needs to add twice the number of the runs of the initial design and, therefore, it is more cost-saving to utilize the semifoldover technique for a three-level design that only needs to add once the number of the original runs. The semifoldover technique was first introduced by Daniel (1962), then Barnett et al. (1997) presented the idea by a case study. Mee and Peralta (2000) studied various cases when semifolding a regular resolution IV and other resolution III designs, and proved that some semifoldover designs are able to estimate as many t
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