New CUSUM and dual CUSUM mean charts

The CUSUM (C) charts are well recognized as a potentially advanced process monitoring tools because of their sensitivity against small and moderate shifts. In this paper, we first improve the sensitivity of the Brownian motion-based C (BC) chart with an appropriate transformation, named new BC (NBC) chart, for monitoring moderate and large shifts in the mean of a normal process. Then, using the control charting structure of the Crosier C (CC) chart, we propose the NBCC (NBC with CC structure) chart. In addition, for efficiently detecting a mean shift within an interval, dual version of these control charts are also proposed, named the dual NBC (DNBC) and dual NBCC (DNBCC) charts. Moreover, the fast initial response feature is also incorporated into the proposed charts. Using the Monte Carlo simulation, the run length properties of the proposed charts are computed. The run length performances of the existing and proposed charts are compared using the extra quadratic loss and integral relative average run length as performance criterion. It turns out that the NBC and NBCC (DNBC and DNBCC) charts are uniformly more sensitive than the C, CC, and NBC (dual C and dual CC) charts when detecting the mean shifts in small, moderate, and large intervals, where the DNBCC chart outperforms all considered charts. The proposed charts are also applied on real data sets to support the proposed theory.