An optimisation design of the combined np-CUSUM scheme for attributes

The np chart and the binomial cumulative sum (CUSUM) chart are attribute charts that monitor the fraction non-conforming p. While the np chart is effective for detecting large process shifts in p, the CUSUM chart is more powerful for detecting small and moderate p shifts. This article presents an optimisation algorithm for the design of the combined np chart and CUSUM chart (the np-CUSUM scheme). This design algorithm not only optimises the charting parameters of the np chart element and CUSUM chart element, but also optimises the allocation of detection power between the two chart elements, so that the best overall performance can be achieved. The np-CUSUM scheme has the salient features of the np chart and the CUSUM chart. The performance of the np-CUSUM scheme is compared with that of other charts in a systematic and quantitative manner. The results show that the optimal np-CUSUM scheme always outperforms, or at least performs equally as, the individual np chart, CUSUM chart and binomial exponentially weighted moving average (EWMA) chart by 222%, 5% and 11%, respectively, in terms of the average number of defectives (AND), under different conditions. [Received 30 November 2010; Revised 21 February 2011; Accepted 3 May 2011]