Analysis and optimization of split-plot operating window experiments: Methodology and application

Abstract

The method of Operating Window (OW) is a statistical-engineering approach to improve the robustness and reliability of products/processes. Like many industrial experiments, operating window experiments are often conducted with a split-plot structure in order to accommodate the nature of some experimental factors. Existing research on OW has paid little attention to this aspect of the OW experiments. In this paper we focus on the modeling and optimization of OW experiments by incorporating the split-plot structure. For ease of reading, we use the ubiquitous paper feeder example to illustrate each step of modeling and optimization. First, we employ the generalized linear mixed effects models (GLMM) to model the complex error structure afforded by the split-plot structure. Then we obtain statistically significant variables for each failure mode in the feeder example: misfeed and multifeed. These analysis results enable us to make inference about the predicted failure probability for each mode. The optimization step is performed by minimizing some performance measures proposed in the literature, especially the one by Joseph and Wu.(1) Performance measures for each control run are calculated and then modeled in terms of the identified control variables, which lead to the identification of optimal settings of these variables. This case study not only reveals the split-plot structure common in industrial experiments and identify the key factors for the process, but also provides some additional insights on the process.