A Comparison of Shewhart Control Charts based on Normality, Nonparametrics, and Extreme-Value Theory

Several control charts for individual observations are compared. The traditional ones are the well-known Shewhart control charts with estimators for the spread based on the sample standard deviation and the average of the moving ranges. The alternatives are nonparametric control charts, based on empirical quantiles, and some new control charts based on kernel estimators, and extreme-value theory. The use of all presented control charts is shown by a practical example, and their performance is studied by simulation. It turns out that most alternative control charts are not only robust against distributional assumptions but also reasonably good under the normality assumption. The performance of our Alternative Empirical Quantile control chart is excellent for all distributions considered.