The purpose of order-of-addition (OofA) experiments is to identify the best order in a sequence of m components in a system. Such experiments may be analyzed by various regression models, the most popular ones being based on pairwise ordering (PWO) factors or on component-position (CP) factors. This paper reviews these models and extensions and proposes a new class of models based on response surface (RS) regression using component position numbers as predictor variables. Using two published examples, it is shown that RS models can be quite competitive. In case of model uncertainty, we advocate the use of model averaging for analysis. The averaging idea leads naturally to a design approach based on a compound optimality criterion assigning weights to each candidate model.

中文翻译：

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加法顺序实验的回归模型

加法顺序 (OofA) 实验的目的是确定系统中m个组件序列中的最佳顺序。此类实验可以通过各种回归模型进行分析，最流行的回归模型基于成对排序 (PWO) 因素或组件位置 (CP) 因素。本文回顾了这些模型和扩展，并提出了基于响应面 (RS) 回归的一类新模型，使用组件位置数作为预测变量。使用两个已发布的示例，表明 RS 模型可以很有竞争力。在模型不确定的情况下，我们提倡使用模型平均进行分析。平均的想法自然会导致一种基于复合最优性标准的设计方法，该标准为每个候选模型分配权重。