Statistical quality control using image intelligence: A sparse learning approach

Advances in image acquisition technology have made it convenient and economic to collect large amounts of image data. In manufacturing and service industries, images are increasingly used for quality control purposes because of their ability to quickly provide information about product geometry, surface defects, and nonconforming patterns. In production line monitoring, image data often take the form of image streams in the sense that images from the process are being collected over time. In such applications, a fundamental task is to properly analyze image data streams. This image monitoring problem is challenging for several reasons. First, images often have complicated structures such as edges and singularities, which render many traditional smoothing methods inapplicable. Second, a typical grayscale image contains tens of thousands of pixels, so the data is high‐dimensional. It has been shown in the statistical process control (SPC) literature that conventional multivariate control charts have limited power of detecting process shifts when the data dimension is high. In this article, we propose to transform images using a two‐dimensional wavelet basis and monitor the wavelet coefficients by sparse learning‐based multivariate control charts. By adapting the sparse learning algorithm to our quality control problem, the proposed method is able to detect shifts in the wavelet coefficients in a timely fashion and simultaneously identify those shifted coefficients. Combining this feature with the localization property of the wavelet basis, our method also enables accurate diagnosis of faulty image regions. In addition, the proposed charting statistics have explicit formulas, so they are easy to compute. Theoretical justifications and numerical comparisons with an existing method show that our method works well in applications.