Summary: Theoretical studies demonstrated that the variable sampling interval (VSI) \(\overline{X}\) charts give substantially faster detection of most process mean shifts than traditional \(\overline{X}\) charts. The standard VSI \(\overline{X}\) chart allows the long and short sampling intervals to be interchangeably used in the practical operation of the chart based on the information of the last sample mean. However, frequent switching between the long and short sampling intervals can be a complicating factor in the application of control charts. Some switching rules have been presented and studied in the literature to improve the situation of frequent switching.
In the present paper, a switching rule based on moving average (MA) is proposed for the VSI \(\overline{X}\) chart. The advantages of moving average are not only to involve the recent several sample means, but also to consider the magnitude of deviation of these sample means from the centerline, which is not included by the switching rules in the literature.
A computer simulation approach is applied to evaluate the performance of the proposed VSI \(\overline{X}\) chart with MA rule. From the simulation results, it can be seen that for a small process mean shift, the VSI \(\overline{X}\) chart with MA rule is always superior to the other types of VSI \(\overline{X}\) charts.