(X)over-bar chart with variable sample size and sampling intervals

Recent theoretical studies have shown that the (X) over bar chart with variable sampling intervals (VSI) and the (X) over bar chart with variable sample size (VSS) are quicker than the traditional (X) over bar chart in detecting shifts in the process. This article considers the (X) over bar chart with variable sample size and sampling intervals (VSSI). It is assumed that the amount of time the process remains in control has exponential distribution. The properties of the VSSI (X) over bar chart are obtained using Markov chains. The VSSI (X) over bar chart is even quicker than the VSI or VSS (X) over bar charts in detecting moderate shifts in the process.