ON ORDERING PROBLEMS: A STATISTICAL APPROACH

Jianbin Chen, Xiaoxue Han, Dennis K.J. Lin, Liuqing Yang, Yongdao Zhou*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In ordering problems, the goal is to find the optimal order. Each experimental run of an order problem is a permutation of m components. Because m! is typically large, it is necessary to select a subset of the m! sequences. Existing selection methods are based on parametric models. However, it is difficult to determine a good approximate model for an ordering problem before collecting the experimental data. With this in mind, we propose a method for choosing the subset for searching for the optimal order without assuming a prespecified model. The proposed method explores the inherent characteristics of the possible orders by using the distance between the positions of the components. We propose a systematic construction method for selecting a subset with a flexible run size, and also show its optimality. Compared with existing model-based methods, the proposed method is more appropriate when the model choice is not clear a priori.

Original languageEnglish
Pages (from-to)1903-1922
Number of pages20
JournalStatistica Sinica
Volume33
Issue number3
DOIs
Publication statusPublished - Jul 2023
Externally publishedYes

Keywords

  • Design of experiments
  • fractional order of addition design
  • pair-wise ordering distance

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