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Monitoring the coefficient of variation (CV) is an effective approach to monitor a process when both the process mean and the standard deviation are not constant but, nevertheless, proportional. Until now, few contributions have investigated the monitoring of the CV for short production runs. This paper proposes an adaptive Shewhart control chart implementing a variable sample size (VSS) strategy in order to monitor the coefficient of variation in a short production run context. Formulas for the truncated average run length are derived. Moreover, a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV in order to evaluate the performance of each chart in a short run context. An example illustrates the use of this chart on real data.