A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean

The usual practice of using a control chart to monitor a process is to take samples from the process with fixed sampling interval (FSI). In this paper, a synthetic (X) over bar control chart with the variable sampling interval (VSI) feature is proposed for monitoring changes in the process mean. The VSI synthetic (X) over bar chart integrates the VSI (X) over bar chart and the VSI conforming run length (CRL) chart. The proposed VSI synthetic (X) over bar chart is evaluated using the average time to signal (ATS) criterion. The optimal charting parameters of the proposed chart are obtained by minimizing the out-of-control ATS for a desired shift. Comparisons between the VSI synthetic (X) over bar chart and the existing X, synthetic X, VSI (X) over bar and EWMA (X) over bar charts, in terms of ATS, are made. The ATS results show that the VSI synthetic (X) over bar chart outperforms the other X type charts for detecting moderate and large shifts. An illustrative example is also presented to explain the application of the VSI synthetic (X) over bar chart.