This thesis is an extension of the work on variable sampling charts (VSI) for monitoring a single parameter. An attempt is made to develop a chart which can simultaneously monitor both the process mean and process variance. The chart is based on a statistic which combines both mean and variance. After developing such a chart variable sampling intervals are introduced and it is evaluated against alternative methods of monitoring mean and variance with variable sampling intervals. The statistic chosen is an approximate statistic and simulation studies are performed for the evaluation. The results are at times counter-intuitive thus an analysis of the properties of the chart is made and explanations are provided.