An adaptive CUSUM chart with single sample size for monitoring process mean and variance

This article proposes an adaptive absolute cumulative sum chart (called the adaptive ACUSUM chart) for statistical process control. The new development includes the variable sampling interval (VSI), variable sample size (VSS) and VSS and interval (VSSI) versions, all of which are highly effective for monitoring the mean and variance of a variable x by inspecting the absolute sample shift x̄-μ0 (where μ0 is the in-control mean or target value of x). While the adaptive ACUSUM chart is a straightforward extension of the ABS CUSUM chart developed by Wu, et al., it is much more effective than all other adaptive CUSUM charts. Noteworthily, the superiority of VSI ACUSUM chart over the best adaptive CUSUM chart in literature is about 35% from an overall viewpoint. Moreover, the design and implementation of the adaptive ACUSUM chart are much simpler than that of all other adaptive CUSUM schemes. All these desirable features of the adaptive ACUSUM chart may be attributable to the use of a single sample size (n = 1). Another quite interesting finding is that the simpler VSI ACUSUM chart works equally well as the more complicated VSSI ACUSUM chart.