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 (d t −d 0) is replaced by (d t −d 0)2 in the formulation of the cumulative sum C t (where d t and d 0 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 p 0. 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).