Monitoring defects on products' surface by incorporating scan statistics into process monitoring procedures

Monitoring the number of defects in constant‐size units is a well‐defined problem in the industrial domain and usually, the control chart is used for monitoring the total number of defects in a product or a sample of products. The c‐chart tracks the total number of defects in each case by assuming that the underlying number of defects (single or several different types of defects) follows approximately the Poisson distribution. An interesting class of problems where the ‐chart is used is when the number of defects in a surface is of interest. Although the number of defects on the surface of products characterizes the quality of the products, it is especially important how concentrated the defects are in specific parts of the product. In this paper, we introduce a scan‐based monitoring procedure, which simultaneously combines control charts for monitoring the evolvement of the number of defects (in general, events) through time and scan statistics for exploring the spatial distribution of defects. The numerical illustration showed that the new procedure has excellent performance under different scenarios.