Detection of location and dispersion effects from partially replicated two-level factorial designs

During the preliminary stage of a quality improvement process, identification of active location and dispersion effects is an important issue. After understanding the impacts of different factorial effects on the system response, a quality engineer can improve the system performance by adjusting the levels of identified factors. Based on the concept of generalized inference, a new testing procedure is proposed in this article; it can be used to identify active location effects from partially replicated two-level factorial designs. Moreover, a two-stage procedure is introduced for integrating the analyses of location and dispersion effects. Two real-world data sets are analyzed for illustrating our method. Based on the simulation results, it is further shown that the proposed method can maintain the empirical size sufficiently close to the nominal level and have satisfactory power. In addition, a catalog of partially replicated designs with a repeated quarter fraction is generated for practical applications.

在质量改进流程的初步阶段，识别显著位置效应与离散效应是一项核心议题。在明确各类因子效应对系统响应的影响后，质量工程师可通过调整已识别因子的水平来优化系统性能。本文基于广义推断（generalized inference）理念提出了一种全新的检验流程，可用于从部分重复二水平析因设计中识别显著位置效应。此外，本文还提出了一种两阶段流程，用于整合位置效应与离散效应的分析工作。本文通过两个真实数据集对所提方法进行了示例验证。基于仿真实验结果，本文进一步证明所提方法可将经验显著性水平维持在足够接近名义水平的区间，且具备优异的检验功效。此外，本文还生成了一类含重复四分之一分部的部分重复设计目录，以供实际应用参考。