Several control charts for individual observations are compared. Traditional ones are the well-known Shewhart individuals control charts based on moving ranges. Alternative ones are non-parametric control charts based on empirical quantiles, on kernel estimators, and on extreme-value theory. Their in-control and out-of-control performance are studied by simulation combined with computation. It turns out that the alternative control charts are not only quite robust against deviations from normality but also perform reasonably well under normality of the observations. The performance of the Empirical Quantile control chart is excellent for all distributions considered, if the Phase I sample is sufficiently large.