HOMOGENEOUSLY WEIGHTED MOVING AVERAGE CONTROL CHART UNDER RANKED SET SAMPLING SCHEMES WITH MEASUREMENTS ERROR

Abstract

Control charts are powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. Over the years, statistical process control practitioners have shown that the performance of control charts in identifying the assignable shifts in a process depends on the sampling scheme used in the charts developments. This study proposed an enhancement to the performance of the homogeneously weighted moving average (HWMA) control chart for monitoring the process mean under measurements error. The developed proposed charts are based on the ranked set sampling (RSS), the median ranked set sampling (MRSS), and extreme ranked set sampling (ERSS). The performance of the proposed charts in detecting a shift in the mean vector using average run length (ARL) and standard deviation of the run length (SDRL) were assessed. Also, the overall performance of the charts was studied using the extra quadratic loss (EQL) and the relative average run length (RARL). The simulation study results showed that the proposed charting schemes are more efficient than the performance of the classical HWMA control chart based on simple random sampling (SRS). In particular, the HWMA chart based on the RSS and MRSS scheme performs notably better. A real-life application, concerning the dataset on the fill volume of a soft drink from Pepsi Cola production Company, is also provided to show the implementation of the proposed charts. The result revealed that the proposed charts based on RSS and MRSS gives the first out-of-control point immediately at the 31 st data point, which indicates that the proposed charts detect the shift earlier than the HWMA chart based on SRS which gave the first out-of-control signal immediately at the 33 rd data point.