Modifying a central composite design to model the process mean and variance when there are hard-to-change factors

Summary.  An important question within industrial statistics is how to find operating conditions that achieve some goal for the mean of a characteristic of interest while simultaneously minimizing the characteristic's process variance. Often, people refer to this kind of situation as the robust parameter design problem. The robust parameter design literature is rich with ways to create separate models for the mean and variance from this type of experiment. Many times time and/or cost constraints force certain factors of interest to be much more difficult to change than others. An appropriate approach to such an experiment restricts the randomization, which leads to a split-plot structure. The paper modifies the central composite design to allow the estimation of separate models for the characteristic's mean and variances under a split-plot structure. The paper goes on to discuss an appropriate analysis of the experimental results. It illustrates the methodology with an industrial experiment involving a chemical vapour deposition process for the manufacture of silicon wafers. The methodology was used to achieve a silicon layer thickness value of 485 Å while minimizing the process variation.