A combined Shewhart-CUSUM chart with switching limit. Issue Volume 31:Issues 2(2019) (3rd April 2019) - Ottenstreuer, Sebastian; Weiß, Christian H.; Knoth, Sven
Abstract: The common Shewhart-cumulative sum (CUSUM) chart deploys an additional Shewhart limit to expand a single CUSUM chart by triggering quick alarms for large changes in the parameter of interest. We utilize this supplementary limit to initiate the CUSUM accumulation, that is, switching between an accumulation phase and a silent phase. The new switching limit's value resides between the reference value of the CUSUM chart and the usual Shewhart limit. Thus, for the case that the CUSUM statistic is equal to zero, a further observation has to be more substantial than this new limit to engage the summing process. We demonstrate the setup and analyze the new combination for independent Poisson distributed data as well as for a more involved time series model with Poisson marginals, namely, the Poisson first-order integer-valued autoregressive model. Moreover, we also consider a real data set from semiconductor industry with apparently overdispersed counts as well as the application to Gaussian variables data. It turns out that the new chart features patterns between a pure CUSUM and a stand-alone Shewhart chart. Hence, it is a solid alternative to both single charts and the ordinary Shewhart-CUSUM chart.