Spatial-nonparametric regression: an approach for monitoring image data

Statistical process control plays a significant role in manufacturing industries as processes become more advanced and manufactured products more complex. Because of the increasing sensitivity of the processes and the inadequacy of the methods based on human inspection, use of product images in statistical process control has been considered by some researchers. In this paper, a regression-based method is developed to monitor image data under two-scale analysis. In the first scale, wavelet transformation is used to extract the main features of geometric profile created from the images. The next scale is to monitor the small-scale components which could be expressed by correlation in error terms. To monitor correlation in error terms, a parametric method is developed. Parameters of the parametric model including spatial correlation coefficient and error term variance are estimated using Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators, respectively. After extracting features for both scales, some appropriate test statistics are computed. Then, monitoring the process is performed by plotting these test statistics on corresponding control charts. Performance of the proposed method is evaluated in terms of run length measures and the difference between the actual value and the estimated value of change-points. Simulation studies are performed on tile images, and the results show the capability of the proposed method in detecting out-of-control conditions and estimating the change-point. The results also indicate the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identifying the source of variability.