On designing CUSUM charts using ratio-type estimators for monitoring the location of normal processes

Document Type : Article


1 a. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai 200240, China. b. Department of Statistics, Government College University Faisalabad, Faisalabad 38000, Pakistan

2 Department of Statistics, Faculty of Sciences, King Abdulaziz University, Jeddah 21551, Saudi Arabia


Control chart is one of the important tools in statistical process control (SPC) that plays a significant role in monitoring and identifying disturbances of any production process. The Shewhart, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) are commonly used control charts for detecting process shifts. CUSUM and EWMA chart are more sensitive in detecting smaller shifts whereas the typical Shewhart chart is known to be only sensitive to large process shifts. The present study incorporates ratio-type estimators based on auxiliary information in CUSUM structure as a substitute of simple mean estimator for monitoring process location. These estimators are more efficient than the simple mean estimator in the presence of high correlation between the study and the auxiliary variables. Average run length (ARL), standard deviation of run length (SDRL) and extra quadratic loss (EQL) are used to measure the performances of the proposed charts. The performance comparison of the proposed chart with the existing CUSUM, CUSUM-FIR and many other control charts are made by using out-of-control ARL. The comparison revealed the superiority of the suggested charts over the other existing charts. An illustrative example is also provided for the performance evaluation of the proposed charts.


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