Statistical process control procedures for functional data with systematic local variations

Many engineering studies for manufacturing processes, such as for quality monitoring and fault detection, consist of complicated functional data with sharp changes. That is, the data curves in these studies exhibit large local variations. This article proposes a wavelet-based local random-effect model that characterizes the variations within multiple curves in certain local regions. An integrated mean and variance thresholding procedure is developed to address the large number of parameters in both the mean and variance models and keep the model simple and fit the data curves well. Guidelines are provided to select the regularization parameters in the penalized wavelet-likelihood method used for the parameter estimations. The proposed mean and variance thresholding procedure is used to develop new statistical procedures for process monitoring with complicated functional data. A real-life case study shows that the proposed procedure is much more effective in detecting local variations than existing techniques extended from methods based on a single data curve.