A Phase Ⅱ nonparametric adaptive exponentially weighted moving average control chart

摘要

The in-control average run-length (ICARL) is often the metric used to design and implement a control chart in practice. To this end, the ICARL robustness of a control chart, that is, how well the chart maintains its advertised nominal ICARL value, under violations of the underlying assumptions, is crucial. Without the ICARL robustness, the shift detection property of the chart becomes questionable. In this article, first, the ICARL robustness of the well-known adaptive exponentially weighted moving average (AEWMA) chart of Capizzi and Masarotto (2003) is examined, in an extensive simulation study, with respect to the underlying assumption of normality. The ICARL profiles of the AEWMA chart are calculated for a range of distributions of various shapes, including light-tailed, heavy-tailed, symmetric, and skewed. Our results show that the AEWMA chart is quite sensitive to the normality (shape) assumption and may not maintain the nominal ICARL under non-normality. Motivated by this, a distribution-free (nonparametric) analog of the AEWMA chart (called the NPAEWMA chart), based on the Wilcoxon rank sum statistic, is proposed for Phase I applications when a Phase I reference sample is available. The NPAEWMA chart shows good ICARL-robustness against non-normality and shift detection capacity.