Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

Two-level orthogonal arrays of strength 3 permit the study of the main effects and the two-factor interactions of the experimental factors. These arrays are classified into regular and nonregular designs. Good regular designs are available in the literature for large run sizes that are a power of 2. In contrast, good nonregular designs, which have run sizes that are multiples of 8 and are more flexible alternatives to regular designs, are not available for large numbers of runs because their construction is challenging. In this article, we introduce a collection of strength-3 nonregular designs with large run sizes that, to the best of our knowledge, have not been explored before in the design literature. Using theoretical results and algorithmic approaches, we construct nonregular designs with up to 1280 runs. Our designs fill the gaps between the available strength-3 designs with large run sizes and outperform many comparably sized benchmark designs in terms of the aliasing among the two-factor interactions. We show the applicability of our collection of strength-3 designs using an infrared sensor experiment. Supplementary materials for this article are available online.强度为3的两水平正交表（two-level orthogonal arrays）可用于探究实验因子的主效应与两因子交互效应。此类正交表可划分为正则设计（regular design）与非正则设计（nonregular design）两类。现有试验设计文献中，针对试验次数为2的幂次的大规模试验，已存在若干优良的正则设计方案。与之相对，优良的非正则设计的试验次数为8的倍数，是正则设计更具灵活性的替代方案，但由于构造难度较高，目前尚无适用于大试验次数的优良非正则设计。本文提出一批试验次数可观的强度3非正则设计，据我们所知，这类设计在现有试验设计文献中尚未被系统研究。本文借助理论推导与算法手段，构造出试验次数最高可达1280的非正则设计。本研究提出的设计填补了现有大试验次数强度3设计之间的空白，且在两因子交互效应混叠程度方面，优于众多规模相当的基准设计。本文通过一项红外传感器试验，验证了所提出的强度3非正则设计集合的实用性。本文的补充材料可在线获取。