Profile Monitoring Based On Functional Mixed Effect Models

In some certain SPC applications, quality of process can not be characterized by a single or several indexes. Instead, they should be represented by the functional relation-ship between a responsible variable and one or more explanatory variables. That is, at each sampling points, what we actually observed is a curve or profile. Profile monitoring is for checking the stability of this relationship over time. In this paper, based on functional mixed effect models (FMM), we proposed a multivariate Profile control chart, which can avoid "curse of dimensionality" in multivariate functions. In order to monitor manufac-turing process with correlation within profiles, this paper incorporate penalized spline and the exponential weighted moving average into Phase II monitoring. Combining with variance function, we construct monitoring statistics, which can not only accommodate correlation within profiles and arbitrary designs, but also get some excellent properties of EWMA control chart. As FMMS provide a flexible and powerful framework for model-ing complex profiles, the novel control chart can be widely used in practice. Numerical stimulations show that the novel scheme can detect shifts efficiently. Compared with parametric chart, this procedure possesses the property of robust-although the type of OC model changes, our proposed chart can still detect drifts efficiently.