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.