A binomial CUSUM chart for detecting large shifts in fraction nonconforming

This article studies a unique feature of the binomial CUSUM chart in which the difference (dt-d0) is replaced by (dt-d0)2 in the formulation of the cumulative sum Ct (where dt and d0 are the actual and in-control numbers of nonconforming units, respectively, in a sample). Performance studies are reported and the results reveal that this new feature is able to increase the detection effectiveness when fraction nonconforming p becomes three to four times as large as the in-control value p0. The design of the new binomial CUSUM chart is presented along with the calculation of the in-control and out-of-control Average Run Lengths (ARL0 and ARL1).