On Efficient Skewness Correction Charts under Contamination and Non-normality

Shewhart control charts are very popular in a variety of disciplines such as industry, agriculture and medical science. The design structure of the usual Shewhart charts depends on normality and one point decision rule. This makes the scope of these charts quite limited and not very efficient for small shifts. This study comes up with an intermediate solution by implementing runs rules schemes and adjusting the limits' coefficients for non-normality using the idea of skewness correction. We have covered some commonly used location and dispersion charts, namely X¯, R and S charts. We have investigated the performance of the proposals in terms of false alarm rate and signalling probability. We have observed that the proposals serve the dual purpose in terms of robustness and efficiency. The study also provides an application example using numerical dataset.