The combined Shewhart–EWMA sign charts

Abstract

The Shewhart control chart is a prominent tool for identifying the changes in process parameters that are of large magnitude, however, it has reduced ability to identify the process changes of small magnitudes. On the other hand, an exponentially weighted moving average (EWMA) control chart is superior to the Shewhart chart in identifying process changes of small magnitudes but it is less proficient than the later chart in identifying changes of large magnitudes. This paper suggests nonparametric combined Shewhart‐EWMA (CSE) charts based on the sign statistic for the process location and process dispersion. The statistical performance measures of these charts are obtained using a Markov chain approach. The numerical comparisons revealed that the performance of a CSE chart lies within the range of the Shewhart sign and EWMA sign charts for identifying a process change of any magnitude. A real‐data example is provided to illustrate the mechanism of the chart.