Complete reliance on the fitted model in response surface experiments is risky and relaxing this assumption, whether out of necessity or intentionally, requires an experimenter to account for multiple conflicting objectives. This work provides a methodological framework of a compound optimality criterion comprising elementary criteria responsible for: (i) the quality of the confidence region-based inference to be done using the fitted model (DP-/LP-optimality); (ii) improving the ability to test for the lack-of-fit from specified potential model contamination in the form of extra polynomial terms; and (iii) simultaneous minimisation of the variance and bias of the fitted model parameters arising from this misspecification. The latter two components have been newly developed in accordance with the model-independent 'pure error' approach to the error estimation. The compound criteria and design construction were adapted to restricted randomisation frameworks: blocked and multistratum experiments, where the stratum-by-stratum approach was adopted. A point-exchange algorithm was employed for searching for nearly optimal designs. The theoretical work is accompanied by one real and two illustrative examples to explore the relationship patterns among the individual components and characteristics of the optimal designs, demonstrating the attainable compromises across the competing objectives and driving some general practical recommendations.

翻译：在响应面实验中完全依赖拟合模型存在风险，而放宽这一假设——无论是出于必要还是有意为之——都需要实验者考虑多个相互冲突的目标。本文提出了一种复合最优性准则的方法论框架，该准则由若干基础准则组成，分别负责：(i) 基于拟合模型的置信区域推断的质量（DP-/LP-最优性）；(ii) 提升针对指定潜在模型污染（以额外多项式项形式存在）的失拟检验能力；以及(iii) 同时最小化由模型误设引起的拟合模型参数的方差与偏差。后两个组成部分是依据与模型无关的"纯误差"误差估计方法新近开发的。复合准则与设计构建被适配于受限随机化框架：即区组设计与多层级实验，其中采用了逐层级分析方法。本文采用点交换算法搜索近似最优设计。理论工作辅以一个真实案例和两个示例性案例，用以探究最优设计中各组成部分与特征之间的关系模式，展示在竞争目标之间可实现的权衡，并推导出若干通用实践建议。