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<p>In recent years, order-of-addition experiments have gained significant attention due to their efficiencies in determining the impact of sequence orders on the response of interest. When the number of components is large, the full design requires <i>m</i>! runs, which becomes impractical for applications. Consequently, constructing efficient fractional designs is strongly needed. Component orthogonal arrays, due to their optimality and balanced structures, are widely used as fractional designs of full designs. Existing component orthogonal arrays are either restricted in the case where the number of components is a prime or prime power, or suffered from excessively large run sizes. In this paper, we establish relationships between component orthogonal arrays and two special structures in group theory. Building upon these connections, two general methods to construct component orthogonal arrays are proposed. A detailed comparison with existing methods demonstrates that the proposed methods support a broader range of number of components while maintaining small run sizes. Specially, the smallest component orthogonal arrays when the number of components is less than 12 can be constructed.</p>

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Construction of component orthogonal arrays with flexible sizes

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Chengjun Hou,
  • Min-Qian Liu,
  • Liuqing Yang

摘要

In recent years, order-of-addition experiments have gained significant attention due to their efficiencies in determining the impact of sequence orders on the response of interest. When the number of components is large, the full design requires m! runs, which becomes impractical for applications. Consequently, constructing efficient fractional designs is strongly needed. Component orthogonal arrays, due to their optimality and balanced structures, are widely used as fractional designs of full designs. Existing component orthogonal arrays are either restricted in the case where the number of components is a prime or prime power, or suffered from excessively large run sizes. In this paper, we establish relationships between component orthogonal arrays and two special structures in group theory. Building upon these connections, two general methods to construct component orthogonal arrays are proposed. A detailed comparison with existing methods demonstrates that the proposed methods support a broader range of number of components while maintaining small run sizes. Specially, the smallest component orthogonal arrays when the number of components is less than 12 can be constructed.