Recently, simultaneous monitoring of process mean and variability has gained increasing attention. By departing from the accurate measurements assumption, this paper investigates the effect of gauge measurement errors on the performance of the maximum generally weighted moving average (Max-GWMA) chart for simultaneous monitoring of process mean and variability under an additive covariate model. Multiple measurements procedure is employed to compensate for the undesired impact of gauge inaccuracy on detection capability of the Max- GWMA chart. Simulation experiments in terms of average run length (ARL) are conducted to assess the power of the developed chart to detect different out-of-control scenarios. The results confirm that the gauge inaccuracy affects the sensitivity of the Max-GWMA chart. Moreover, the results show that taking multiple measurements per item adequately decreases the adverse effect of measurement errors. Finally, a real-life example is presented to demonstrate how measurement errors increases the false alarm rate of the Max-GWMA chart.