Performance of the mean control charts with generalized sensitizing rules for various probability distribution

The current study highlights and resolves the issues of mean control charts with sensitizing rules. The average run length (ARL)-based mean control charts with sensitizing rules involve a restricted assumption of normality. The restricted assumption has a limitation that in-control ARL deviates from the predefined level when it is violated. Also, false alarm rate (FRL)-based mean control charts with sensitizing rules for various probability distribution results into undesired run length properties. In this study, ARL-based mean control charts (two-sided and one-sided) with generalized sensitizing rules for normal and non-normal distributions are derived. Results indicate that in-control ARL is obtained equal to the predefined level. This shows that the proposed mean control charts have sustained behavior for any choice of sensitizing rules and probability distribution. In addition, we have explained that an optimal choice of the sensitizing rules depend on a process probability distribution. Besides, the proposed control charts are applied in petrochemical process to monitor the diesel oil characteristics.