Abstract
The use of run rules alongside traditional control limits as a sensitizing method has been suggested in the literature in order to increase the power of control charts. Assessment on the effect of combining different run rules with Phase II control charts have been carried out both in parametric and nonparametric approaches with good results, although some controversy exists when using run rules in combination with Phase II monitoring statistics. However, the effect of such enhancing methods has been barely explored within Phase I stages, where nonparametric approaches have a key role due to the high levels of uncertainty on the data model. To address this gap, this paper proposes a thorough examination on the state-of-the-art of the implementation of run rules in Shewhart-type nonparametric Phase I control charts. The latter offers sensitivity to large and isolated changes, whereas the former rules improve the assessment of different forms of drifts and change-points. Readers will find guides on the use of run rules, different types of implementations, a discussion on their controversy, and suggestions for future research.