Run and Scan Rules in Statistical Process Monitoring

In this paper, we provide an overview of the use of run and scan rules in statistical process monitoring. Although we focus on control charts, supplemented with various stopping rules based on run and scan statistics, several other monitoring procedures that incorporate run and scan statistics are reviewed as well. Rules based on the notion of scans have been incorporated in the traditional Shewhart charts in order to improve their performance and at the same time preserve their simplicity. In our presentation we review the major types of run and scan rules currently available in the literature of control charts and highlight how they are implemented in practice. A unified framework for studying the characteristics of run- and scan-based control charts by exploiting a Markov chain approach is also provided. We end up with some concluding remarks and some directions for future research in the area under review.