Designs for Order-of-Addition (OofA) experiments have received growing attention due to their impact on responses based on the sequence of component addition. In certain cases, these experiments involve heterogeneous groups of units, which necessitates the use of blocking to manage variation effects. Despite this, the exploration of block OofA designs remains limited in the literature. As experiments become increasingly complex, addressing this gap is essential to ensure that the designs accurately reflect the effects of the addition sequence and effectively handle the associated variability. Motivated by this, this paper seeks to address the gap by expanding the indicator function framework for block OofA designs. We propose the use of the word length pattern as a criterion for selecting robust block OofA designs. To improve search efficiency and reduce computational demands, we develop algorithms that employ orthogonal Latin squares for design construction and selection, minimizing the need for exhaustive searches. Our analysis, supported by correlation plots, reveals that the algorithms effectively manage confounding and aliasing between effects. Additionally, simulation studies indicate that designs based on our proposed criterion and algorithms achieve power and type I error rates comparable to those of full block OofA designs. This approach offers a practical and efficient method for constructing block OofA designs and may provide valuable insights for future research and applications.

翻译：序贯添加（OofA）实验设计因其响应值受组分添加顺序影响而受到日益广泛的关注。在某些情况下，此类实验涉及异质性实验单元组，因此需要使用区组设计来管理变异效应。尽管如此，现有文献中对序贯添加区组设计的探索仍十分有限。随着实验日益复杂，填补这一空白对于确保设计能准确反映添加顺序效应并有效处理相关变异性至关重要。基于此，本文旨在通过扩展序贯添加区组设计的示性函数框架来弥补这一不足。我们提出使用字长型作为选择稳健序贯添加区组设计的准则。为提高搜索效率并降低计算需求，我们开发了采用正交拉丁方进行设计构造与选择的算法，从而最大限度地减少穷举搜索的需要。基于相关性图的分析表明，所提算法能有效管理效应间的混杂与别名现象。此外，模拟研究显示，基于我们提出的准则和算法构建的设计，其检验功效与Ⅰ类错误率与完全序贯添加区组设计相当。该方法为构建序贯添加区组设计提供了一种实用且高效的途径，并可能为未来的研究和应用提供有价值的见解。