Geometric and hidden projection are two important properties to consider for three-level fractional factorials. The effective development of methods that can address tasks involving both these properties requires a unified design framework that integrates them. We highlight one integrative framework that is based on indicator functions for three-level designs under the linear-quadratic parameterization system. We demonstrate the broad scope and utility of this framework by using it to develop a new procedure for addressing a task comprised of three serial problems in geometric and hidden projection. The first in the series is to construct the sets of smallest follow-up runs to a projection of a three-level design that yield specified aliasing relations. Second is to immediately characterize the partial aliasing relations among factorial effects in the resulting augmented designs. The final problem is to identify the augmented designs that maximize popular optimality criteria with respect to the second-order model among all of the candidate augmentations. The application of our procedure is illustrated with sample projections of definitive screening designs onto four, five, and six factors. The integrative framework that we present can ultimately facilitate the systematic development of methods that advance comprehensive understanding of multiple properties for general three-level designs.

几何投影和隐藏投影是三级分数阶乘分解要考虑的两个重要属性。要有效开发能够处理涉及这两个属性的任务的方法，就需要一个将它们集成在一起的统一设计框架。我们重点介绍了一种基于指标函数的集成框架，该指标框架用于线性二次参数化系统下的三级设计。我们通过使用它开发用于解决由几何投影和隐藏投影中的三个系列问题组成的任务的新程序，展示了此框架的广泛范围和实用性。该系列的第一篇文章将构建最小的后续运行集，以生成三级设计的投影，从而产生指定的混叠关系。第二是立即刻画最终增强设计中阶乘效应之间的部分混叠关系。最终的问题是要确定所有候选扩增中相对于二阶模型最大化流行最优标准的扩增设计。最终筛选设计在四个，五个和六个因素上的示例投影说明了我们程序的应用。我们提出的集成框架最终可以促进方法的系统开发，这些方法可以促进对一般三级设计的多种属性的全面理解。最终筛选设计在四个，五个和六个因素上的示例投影说明了我们程序的应用。我们提出的集成框架最终可以促进方法的系统开发，这些方法可以提高对一般三级设计的多个属性的全面理解。最终筛选设计在四个，五个和六个因素上的示例投影说明了我们程序的应用。我们提出的集成框架最终可以促进方法的系统开发，这些方法可以促进对一般三级设计的多种属性的全面理解。