Two-stage Model for Small Mean Shifts Detection

Recently, adaptive CUSUM (ACUSUM) charts have been proposed for detecting a range of mean shifts efficiently by adjusting the reference value dynamically. However, if mean shifts are smaller than a minimum pre-specified shift level, the ACUSUM chart may perform poorly. To overcome this problem, we propose a length limit approach for detecting small mean shifts efficiently. Moreover, we develop a two-stage model that applies a length limit to control charts. Under the two-stage model, two procedures, two-stage procedure with Adapted Regime Shift Index (TARSI) and Two-stage procedure with CUSUM Index (TCI), are implemented. The ARL performance of the proposed procedures is investigated and compared with EWMA, CUSUM, and ACUSUM charts.

J. Kim, M. Park, M.K. Jeong, E.A. Elsayed, A.S Hamouda, K. N. Al-Khalifa