In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence of the components. Extensive research on this topic has been conducted, but almost all designs are found by optimizing the $D-$optimality criterion. However, when prediction of the response is important, there is still a need for $I-$optimal designs. A new model for OofA experiments is presented that uses transition effects to model the effect of order on the response, and the model is extended to cover cases where block-wise constraints are placed on the order of addition. Several algorithms are used to find both $D-$ and $I-$efficient designs under this new model for many run sizes and for large numbers of components. Finally, two examples are shown to illustrate the effectiveness of the proposed designs and model at identifying the optimal order of addition, even under block-wise constraints.

翻译：在化学、制药和食品工业中，有时一组组分的添加顺序会对最终产品产生影响。这类问题属于添加顺序问题，其目标是寻找组分的最优添加序列。尽管已有大量相关研究，但几乎所有设计都是通过优化$D-$最优性准则得到的。然而，当响应预测至关重要时，仍需要$I-$最优设计。本文提出了一种新的添加顺序实验模型，该模型利用过渡效应来刻画顺序对响应的影响，并将模型扩展至存在分块顺序约束的情形。针对多种实验次数和大量组分的情况，采用多种算法寻找该新模型下的$D-$高效和$I-$高效设计。最后通过两个实例表明，即使在分块约束条件下，所提出的设计与模型仍能有效识别最优添加顺序。