Statistical process control procedures for functional data with systematic local variations
针对制造过程中具有尖锐变化的复杂函数型数据，提出基于小波的局部随机效应模型，并开发均值和方差阈值化程序，用于过程监控，在检测局部变化上优于现有方法。
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.