The robustness of Shewhart control charts for subgroup means and subgroup ranges was tested by using the Monte Carlo method using training data sets comprising various numbers of points, with two repetitions in each subgroup (as in routine laboratory practice). The following control chart designs were tested: conventional based on the arithmetic mean and standard deviation, robust based on the median and/or the trimmed mean and Winsorized standard deviation, and a two-step design. The methods were applied to the system in the state of statistical control (outliers excluded) and to the system without statistical control (outliers included). Satisfactory results for both cases were only obtained when using the two-stage control charts. The conventional charts led to underestimation of the effect of outliers in the system without statistical control, whereas the robust control charts led to overestimation of the effect of outliers (false alarm) in the system under statistical control. The tests also gave evidence that the training set should include 20 points as a minimum.