Effect of skewed distributions on Shewhart control chart coefficients

In this paper, we discuss the influence of asymmetric distribution functions on the values of the coefficients of Shewhart control charts (CCS) of the x-mR and -R types. It is argued that for distribution functions (DF) that are very different from the normal law, this influence should be taken into account. The level of such a change in the CCF coefficients, which should be taken into account, is discussed. The simulation results are presented, and an algorithm for applying the CCS in practice is proposed, taking into account the law of data distribution. An example is also given of how the deviation of the FR of data from the normal law changes the boundaries of the KCS for real logistics supply processes. In conclusion, conclusions and ideas for further research are presented.