QQ Models: Joint Modeling for Quantitative and Qualitative Quality Responses in Manufacturing Systems

A manufacturing system with both quantitative and qualitative (QQ) quality responses (as a QQ system) is widely encountered in many cases. For example, in a lapping process of the semiconductor manufacturing, the quality of wafer's geometrical characteristics is often measured by the total thickness variation as a quantitative response and the conformity of site total indicator reading as a binary qualitative response. The QQ responses are closely associated with each other in a QQ system, but current methodologies often model the two types of quality responses separately. This article presents a novel modeling approach, called QQ models, to jointly model the QQ responses through a constrained likelihood estimation. The QQ models can jointly select significant predictors by incorporating inherent features of QQ systems, leading to accurate variable selection and prediction. Both simulation studies and a case study in a lapping process are used to evaluate the performance of the proposed method. Supplementary materials to this article are available online.