Economic statistical design of nonparametric control charts

In this work, we apply the economic statistical design framework to nonparametric control charts. To this end, we develop bounds for the type II error probability, i.e. the false negatives rate, of the nonparametric charts that are then used within the model. We implement the optimization problem defining economic statistical design and use it to find the design parameters of nonparametric control charts. We then compare the behavior of this design with parametric and nonparametric charts on different probability distributions with different values of the distribution parameters. We finally perform a brief analysis of the obtained results that emphasizes the differences between the economic statistical design of parametric and nonparametric control charts. In this study, we also give a number of advantages and shortcomings of both approaches so that the interested reader can make the best possible decision on which control chart it is better to use for a given application.