Abstract

An order-of-addition (OofA) experiment investigates how the sequence

of input factors influences the experimental response. This type of experiment

has recently gain significant interest among practitioners in clinical trials and

industrial processes. In this work, we introduce a new cost-efficient design called

the Complete Consecutive Order-Pairing (CCOP) design. The CCOP design not

only considers the effects of the component order on the response but also simultaneously accounts for the effects due to the component levels. We also propose

a new statistical model associated with the CCOP design for identifying the optimal settings of both component order and levels. The CCOP design method

evaluates the effects of two successive treatments by using the minimal number of

runs, as each pair of level settings for two different components appears exactly

once. Compared to recent studies on OofA experiments, our design effectively

handles pure order experiments and multi-level experiments with a relatively

small run size.

Information

Preprint No.SS-2023-0357
Manuscript IDSS-2023-0357
Complete AuthorsJing-Wen Huang, Frederick Kin Hing Phoa
Corresponding AuthorsFrederick Kin Hing Phoa
Emailsfredphoa@stat.sinica.edu.tw

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Acknowledgments

The authors would like to thank Dr. Yuan-Lung Lin for his suggestions

on the structure of CCOP designs. This work was supported by Academia

Sinica (Taiwan) Thematic Project grant numbers AS-TP-109-M07 and AS-

IA-112-M03, and the National Science and Technology Council of Taiwan

grant numbers 111-2118-M-001-007-MY2 and 113-2628-M-001-010-MY3. Huang

is supported by the doctoral student scholarship provided by the Institute

of Statistical Science, Academia Sinica. Part of this work was included in

a chapter of the Ph.D. dissertation of Ms. Jing-Wen Huang. The authors

would also like to thank the reviewers and the editors for their excellent

comments and suggestions to improve the quality of this paper during the

revision.

Supplementary Materials

The supplementary material consists of two appendix sections: (1) Examples, (2) Proof of Theorems, and (3) Simulation and Real Data Analysis

with k = 1 for CP-related Models.

Supplementary materials are available for download.