关键词: 统计过程监控, 质量控制, 图像数据, 异常诊断

Abstract: In many manufacturing sectors, such as LCD panel production, tile manufacturing, and semiconductor fabrication, product surface quality is of crucial importance. With the wide application of machine vision systems, image data composed of pixels with varying gray levels are captured to reflect the surface quality. Product quality in these industries can therefore be characterized by the uniformity within an image (e.g., LCD panels) or the conformity of an image to a predefined pattern (e.g., manufactured tiles). To ensure process and product quality and prevent potential loss, engineers are interested in the timely detection of changes in image uniformity or deviations from the specific pattern. As a vital tool for statistical process monitoring, control charts are increasingly employed in image monitoring for detecting anomalous changes. In the statistical monitoring for image data, there are two main issues of concern. One is the detection of fault occurrence, which is to trigger an alarm for the change in the process as early as possible. This is usually achieved through detecting the shift in the gray levels of pixels in a certain area within an image. The other is the identification of fault location/size, which usually involves the estimation of faulty pixels or regions. Most existing research has mainly focused on either detecting fault occurrence or identifying fault location/size. Simultaneous detection and identification of faults are relatively less explored but are attracting growing research attention.
In order to enhance the rapid detection of fault occurrence and improve the accuracy of fault estimation, this study makes use of the fact that faulty pixels tend to appear as a cluster, and accumulates anomalous changes surrounding the faulty pixels through spatial smoothing. Specifically, a spatial EWMA (Exponentially Weighted Moving Average) is integrated with a temporal EWMA for locating the center of the faulty regions. Starting from the region center, a region growing method can then be applied to effectively identify the faulty regions. By constructing a monitoring statistic for the faulty region only, a signal can be efficiently triggered if a change occurs to the process. Meanwhile, the fault location and size can be readily identified. To implement the proposed spatial-temporal EWMA and region growing based method for image data, three steps are involved.
First, to identify faults of real practical significance and reduce computational difficulty, each image is divided into non-overlapping square regions of equal size. The average gray levels within these divided regions are standardized to facilitate subsequent quality monitoring. Second, the temporal EWMA method is applied to smooth the average gray levels within the individual regions. In this way, temporal shifts are accumulated, and even small shifts in the process can be detected in a more timely manner. Subsequently, the spatial EWMA is imposed on the temporal EWMA statistics, aiming to accumulate possible changes surrounding each region. With such enhancement, faults of even small magnitude can be detected with a higher probability. Among the spatial EWMA values for all the divided regions, the maximum value indicates the region with the most significant change, and is therefore used to identify the center of the shifted regions. Third, with this identified region center as the starting point, a region growing strategy is employed to determine the boundary of the shifted area. A charting statistic is then constructed corresponding to the shifted regions. At each time point, the value of the charting statistic is calculated, and alarms tend to be triggered upon fault occurrence. Furthermore, the location of the shift center and the size of the shifted regions are already available when region growing is implemented.
To evaluate the performance of this approach, extensive simulation experiments are conducted. A total of 150 scenarios is considered, including various combinations of 3 fault center locations, 5 fault sizes, and 10 shift magnitudes. The fault detection and identification performance are evaluated using the steady-state median run length (SSMRL) and median Dice similarity coefficient (MDSC) indicators. The results show that the proposed method is superior to the comparative method in accurately estimating the location and size of shifts when the fault size is small, while it enables more rapid shift detection in cases where the fault size is large.
The proposed method leverages the advantage of spatial smoothing in detecting small sized faults, and the power of temporal smoothing in detecting small shifts. With the region growing strategy, the proposed method can be flexibly applied to the detection of both regular and irregular faults, making it highly adaptable to various image monitoring applications. One limitation of this method is that it assumes only one single fault occurs. Future research endeavors may explore the extension of this method to detect multiple faults.

Key words: statistical process monitoring, quality control, image data, fault diagnosis