A combined synthetic&X chart for monitoring the process mean

Abstract

The Shewhart X chart (or X chart) is widely used to monitor the mean of a quality characteristic x. This chart decides the process status based on the magnitude of the sample mean x and is effective for detecting large mean shifts. The synthetic chart is also a Shewhart type chart for monitoring the process mean, but it utilises the information about the time interval between two nonconforming samples. Here a sample is nonconforming if its x value falls beyond the predetermined warning limits. Unlike the X chart, the synthetic chart is more powerful to detect small shifts. The applications of the X and synthetic charts cover a wide variety of manufacturing processes and production lines, e.g., the monitoring of the mean values of the inside diameter of a piston-ring, the viscosity of aircraft paint, the resistivity of silicon wafers. This article proposes a combined scheme, the Syn-X chart, that comprises a synthetic chart and an X chart. The results of the performance studies show that the Syn-X chart always outperforms the individual X chart and synthetic chart under different conditions. It is more effective than the X chart and synthetic chart by 47% and 20%, respectively, over the wide range of mean shift values in different experiment runs.