A Joint Multiresponse Split-Plot Modeling and Optimization Including Fixed and Random Effects

This paper deals with a proposal for joint modeling and process optimization for split-plot designs analyzed through mixed response surface models. It addresses the following main issues: i) the building of a joint mixed responsesurface model for a multiple response situation, by defining only one response through which specific coefficients areincluded for studying the association among the responses; ii) the considering of fixed as well as random effects within a joint modeling and optimization context; iii) the achievement of an optimal solution by involving specific as well as common coefficients for the responses. We illustrate our contribution through a case-study related to a split-plot design on electronic components of printed circuit boards (PCBs); we obtain satisfactory results by confirming the validity of thiscontribution, where the qualitative factor PCB is also studied and optimized.