Introduction of a general class of entropy-based control charts: The Φ-chart

We introduce a new class of Shewhart control charts, namely the f-chart. This new class is based on the cumulative paired f-divergence that generalizes both the cumulative (residual) entropy and the differential entropy. The f-chart contains several subclasses; of which one has a special case, the G-chart, which uses Gini’s mean difference as a measure of dispersion. We investigate the performance of three of the subclasses of f-charts in a showcase scenario, comparing its average run length under the Gaussian and several alternative distributions relevant to process control. We find especially the new Leik control chart to outperform classical Shewhart charts, which are based on ranks, standard deviation, or Gini’s mean difference. The results imply that monitoring a production process using f-charts results in faster detection of out-of-control processes, which can be crucial for a variety of application areas.