A binomial CUSUM chart for detecting large shifts in fraction nonconforming

Abstract

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).

Keywords:

• quality control
• statistical process control
• attribute control chart
• binomial CUSUM control chart
• fraction nonconforming