The statistical design for order-of-addition (OofA) experiments has received much recent interest as its potential in determining the optimal sequence of multiple components, for example, the optimal sequence of drug administration for disease treatment. The traditional OofA experiments focus mainly on the sequence effects of components, that is, the experimenters fix the factor level of each component and observe how the response is affected by varying the sequences of components. However, the components may also have factorial effects in that changing their factor levels in a given sequence can affect the response. In view of this, we consider the design problem for OofA experiments where each component is experimented at two levels. A systematic method is given to construct OofA designs that jointly considers the sequence design and factorial design for all components. By appropriately choosing the sequence and factorial designs, we show that the combination of the two parts results in a balanced design with an economical run size. Moreover, the constructed designs enjoy a number of optimality properties such as -, - and -optimalities under some empirical models. The design method proposed can be extended to some other practical situations like the number of process variables is different from the number of components, and OofA experiments with multilevel components.

中文翻译：

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两级组分的添加顺序实验设计

添加顺序（OofA）实验的统计设计最近引起了人们的广泛关注，因为它在确定多个组分的最佳序列方面具有潜力，例如，用于疾病治疗的最佳给药序列。传统的OofA实验主要关注成分的序列效应，即实验者固定每个成分的因子水平，并观察改变成分的序列如何影响响​​应。然而，这些组件也可能具有因子效应，因为在给定序列中改变其因子水平可能会影响响应。鉴于此，我们考虑 OofA 实验的设计问题，其中每个组件都在两个级别进行实验。给出了构建 OofA 设计的系统方法，该方法共同考虑所有组件的序列设计和因子设计。通过适当选择序列和因子设计，我们表明，这两部分的组合可以产生具有经济运行规模的平衡设计。此外，构建的设计具有许多最优特性，例如-,- 和-一些经验模型下的最优性。所提出的设计方法可以扩展到其他一些实际情况，例如过程变量的数量与组件的数量不同，以及多级组件的OofA实验。