Designs for order-of-addition experiments

ABSTRACT

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.

Keywords:

• D-efficiency
• minimal-point design
• order of addition
• pair-wise ordering

Acknowledgments

We are thankful to the referees for their valuable comments and suggestions which have led to a great improvement in the presentation of this paper. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771220, 11801331, 11771219 and 11701020), National Ten Thousand Talents Program, Tianjin Development Program for Innovation and Entrepreneurship, Tianjin ‘131’ Talents Program, National Science Foundation (Grant No. DMS-18102925), and Natural Science Foundation of Shandong Province (Grant No. ZR2018BA013).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11771220, 11801331, 11771219 and 11701020), National Ten Thousand Talents Program, Tianjin Development Program for Innovation and Entrepreneurship, Tianjin ‘131’ Talents Program, National Science Foundation (Grant No. DMS-18102925), and Natural Science Foundation of Shandong Province (Grant No. ZR2018BA013).