TY - JOUR
T1 - Designs for order-of-addition experiments
AU - Zhao, Yuna
AU - Lin, Dennis K.J.
AU - Liu, Min Qian
N1 - Publisher Copyright:
© 2020 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2021
Y1 - 2021
N2 - The order-of-addition experiment aims at determining the optimal order of adding components such that the response of interest is optimized. Order of addition has been widely involved in many areas, including bio-chemistry, food science, nutritional science, pharmaceutical science, etc. However, such an important study is rather primitive in statistical literature. In this paper, a thorough study on pair-wise ordering designs for order of addition is provided. The recursive relation between two successive full pair-wise ordering designs is developed. Based on this recursive relation, the full pair-wise ordering design can be obtained without evaluating all the orders of components. The value of the D-efficiency for the full pair-wise ordering model is then derived. It provides a benchmark for choosing the fractional pair-wise ordering designs. To overcome the unaffordability of the full pair-wise ordering design, a new class of minimal-point pair-wise ordering designs is proposed. A job scheduling problem as well as simulation studies are conducted to illustrate the performance of the pair-wise ordering designs for determining the optimal orders. It is shown that the proposed designs are very efficient in determining the optimal order of addition.
AB - The order-of-addition experiment aims at determining the optimal order of adding components such that the response of interest is optimized. Order of addition has been widely involved in many areas, including bio-chemistry, food science, nutritional science, pharmaceutical science, etc. However, such an important study is rather primitive in statistical literature. In this paper, a thorough study on pair-wise ordering designs for order of addition is provided. The recursive relation between two successive full pair-wise ordering designs is developed. Based on this recursive relation, the full pair-wise ordering design can be obtained without evaluating all the orders of components. The value of the D-efficiency for the full pair-wise ordering model is then derived. It provides a benchmark for choosing the fractional pair-wise ordering designs. To overcome the unaffordability of the full pair-wise ordering design, a new class of minimal-point pair-wise ordering designs is proposed. A job scheduling problem as well as simulation studies are conducted to illustrate the performance of the pair-wise ordering designs for determining the optimal orders. It is shown that the proposed designs are very efficient in determining the optimal order of addition.
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U2 - 10.1080/02664763.2020.1801607
DO - 10.1080/02664763.2020.1801607
M3 - Article
C2 - 35706467
AN - SCOPUS:85089024832
SN - 0266-4763
VL - 48
SP - 1475
EP - 1495
JO - Journal of Applied Statistics
JF - Journal of Applied Statistics
IS - 8
ER -