The Dynamic Window Approach as a Tool to Improve Performance of Nonparametric Self-Starting Control Charts

The change-point model is an established methodology for the construction of self-starting control charts. Change-point charts are often nonparametric in order to be independent from any specific assumptions about the process distribution. Nonetheless, this methodology is usually implemented by considering all possible splits of a given stream of observations into two adjacent sub-samples. This can make the recent observations too influential and the chart’s signals too dependent on limited evidence. This paper proposes to correct such a distortion by using a window approach, which forces the use of only comparisons based on sub-samples of the same size. The resulting charts are “omnibus”, with respect to their having any kind of shift and also any direction of such shifts. To prove this, this paper focuses on a chart based on the Cramér–von Mises test. We report a simulation study evaluating the average number of readings to obtain a signal after a known shift has occurred. We conclude that, beyond being stable with respect to the direction of the shift, the new chart overcomes its competitors when the distribution heads toward regularity. Finally, the new approach is shown to have successful application to a real problem about air quality.