A variable sampling interval control chart for the coefficient of variation with unknown shift size

Quality has become a universal goal for organizations to sustain competitive merits. Control charts are one of the powerful tools often used by management to achieve cost savings by minimizing process variation and reducing rework, scrap and the need for inspection. However, most of the control charts were proposed based on a deterministic shift size while in reality, practitioners may not know the shift size due to a lack of data. Therefore, this paper develops a variable sampling interval (VSI) chart to monitor the coefficient of variation (CV) with unknown shift size, thereby allowing practitioners to select optimal parameters without specifying the shift size. Optimization design strategies based on the expected average time to signal (EATS), subjected to constraints in terms of the in-control average time to signal (ATS) and in-control average sampling interval (ASI) is presented. The EATS of the chart is numerically compared with its competing charts. The VSI CV chart outperforms the Shewhart CV and synthetic CV charts, while the EWMA-CV2 chart outperforms the VSI CV chart. Significant cost savings can be obtained from a quicker detection of the shift.