A CUSUM scheme with variable sample sizes for monitoring process shifts

The cumulative sum scheme (CUSUM) and the adaptive control chart are two approaches to improve chart performance in detecting process shifts. A weighted loss function CUSUM scheme (WLC) is able to monitor both the mean shift and the increasing variance shift by manipulating a single chart. This paper investigates the WLC scheme with a variable sample sizes (VSS) feature. A design procedure is firstly proposed for the VSS WLC scheme. Then, the performance of the chart is compared with that of four other competitive control charts. The results show that the VSS WLC scheme is more powerful than the other charts from an overall viewpoint. More importantly, the VSS WLC scheme is simpler to design and operate. A case study in the manufacturing industry is used to illustrate the chart application. The proposed VSS WLC scheme suits the scenario where the strategy of varying sample sizes is feasible and preferable to pursue a high capability of detecting process variations.