Order-of-Addition Orthogonal Arrays with High Strength

Shengli Zhao, Zehui Dong and Yuna Zhao
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Shengli Zhao: School of Statistics and Data Science, Qufu Normal University, Qufu 273165, China
Zehui Dong: School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China
Yuna Zhao: School of Mathematics and Statistics, Shandong Normal University, Jinan 250358, China

Mathematics, 2022, vol. 10, issue 7, 1-17

Abstract: In order-of-addition experiments, the full order-of-addition designs are often unaffordable due to their large run sizes. The problem of finding efficient fractional OofA designs arises. The order-of-addition orthogonal arrays are a class of optimal fractional order-of-addition designs for the prevalent pair-wise ordering model, under a variety of widely used design criteria. In the literature, the studies on order-of-addition orthogonal arrays focused on strength 2 while the order-of-addition orthogonal arrays of higher strength have not been investigated yet. In this paper, we focus on order-of-addition orthogonal arrays of strength 3. First, the method of constructing order-of-addition orthogonal arrays of strength 3 is proposed. Second, a theoretical result that states that the order-of-addition orthogonal arrays of strength 3 have better balance properties than those of strength 2 is developed. Third, we provide thorough simulation studies which show that the constructed order-of-addition orthogonal arrays of strength 3 have desirable performance for estimating optimal orders of addition.

Keywords: order-of-addition experiment; orthogonal array; pair-wise ordering model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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