Combined Shewhart CUSUM charts using auxiliary variable

A control chart is an important statistical tool for monitoring disturbances in a statistical process, and it is richly applied in the industrial sector, the health sector and the agricultural sector, among others. The Shewhart chart and the Cumulative Sum (CUSUM) chart are traditionally used for detecting large shifts and small shifts, respectively, while the Combined Shewhart-CUSUM (CSC) monitors both small and large shifts. Using auxiliary information, we propose new CSC (M_iCSC) charts with more efficient estimators (the Regression-type estimator, the Ratio estimator, the Singh and Tailor estimator, the power ratio-type estimator, and the Kadilar and Cingi estimators) for estimating the location parameter. We compare the charts using average run length, standard deviation of the run length and extra quadratic loss, with other existing charts of the same purpose and found out that some of the M_iCSC charts outperform their existing counterparts. At last, a real-life industrial example is provided.