Statistical modeling and monitoring of image data in the presence of temporal and spatial correlations

In this paper, the regression-based approach was developed to monitor image data under two-scale analysis. In the first scale, wavelet transformation was used to extract the main features of geometric profile created from the images. The next scale was to monitor the small-scale components which could be expressed by correlation in error terms. To monitor correlation in error terms, one parametric and one non-parametric methods were developed. Parameters of the parametric model including spatial correlation coefficient and error term variance were estimated using Ordinary Least Squares (OLS) and Generalized Least Squares (GLS) estimators, respectively. In non-parametric method, no assumption was made about the structure of correlation in error terms. To extract useful information about the nature of correlation in error terms, Functional Principal Component Analysis (FPCA) was used. After extracting features for both scales, some appropriate test statistics were computed. Then, monitoring the process was performed by plotting these test statistics on corresponding control charts. Simulation and industrial case studies were also performed to evaluate the proposed method’s performance in detecting different shifts. The results indicated the proper performance of the proposed method in monitoring industrial processes to detect out-of-control conditions and identify the source of variability.