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

Summary: 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.

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  • Topics: Statistical Process Control (SPC)
  • Keywords: Manufacturing process, Modeling, Regression, Prediction, Variable selection, Residuals
  • Author: Deng, Xinwei; Jin, Ran
  • Journal: Technometrics