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

Abstract

Owing to 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, the regression-based approach was developed to monitor image data under two-scale analysis, large-scale and small-scale. Because geometric profiles created from images have complex and non-linear behaviour, wavelet transformation was used to extract the main features (regression coefficients) under large-scale analysis. Observations in mentioned profiles could be temporally or spatially correlated as well. To monitor the small-scale components which could be expressed by correlation in error terms, one parametric and one nonparametric methods were developed. 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. Performance of the proposed method was evaluated in terms of run-length and change-point measures. 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.