The Shewhart Sign Chart with Ties: Performance and Alternatives

The Shewhart Sign (SN) control chart is a well-known distribution-free statistical process monitoring tool due to its robustness to the violation of the normality assumption for observations. To the best of our knowledge, there is not yet a thorough understanding of what happens to the statistical properties of the SN control chart in the presence of observations tied to the monitored population quantile, for example, themedian: this is an event occurring in practice, in particularwhen the process runs in-control, because of the measurement device resolution, which inevitably introduces a rounding-off error. In this paper, we tackle the problem and show that when ties occur, the Shewhart SN control chart is no longer distribution-free, even in the presence of a small probability of having ties. To solve the problem, we discuss some procedures to handle the occurrence of ties. The study shows that the best strategy simply consists in implementing a Bernoulli trial approach: in practice, ties are reconsidered by 50% chance as being greater or smaller than the monitored population quantile. We quantitatively show that this approach allows the distribution-free properties of the Shewhart SN to be generally preserved.