Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process is introduced. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carrited out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.Statistical quality control charts were introduced in the early work of Shewhart (1926) and since then several variations of them have been proposed for monitoring continuous characteristics. Most of the control charts are distribution-based procedures in the sense that the process output is assumed to follow a specified probability distribution (usually normal); see, for example, Albers et al. (2004).