Optimal Designs of the Group Runs Exponentially Weighted Moving Average XbarX and t Schemes

The analysis of an X$\bar{X} $ scheme often assumes that the process standard deviation is accurately assessed and remains constant. However, in practice, this is rarely true. Noting that the group runs (GR) scheme performs better than the synthetic scheme, in this research, we proposed the GR exponentially weighted moving average (GR EWMA) X$\bar{X} $ and t schemes and determined their true optimal parameters using the optimisation programmes. Our findings indicate that similar to the synthetic EWMA X$\bar{X} $ scheme, the proposed GR EWMA X$\bar{X} $ scheme is not resilient to errors in the estimation of the standard deviation of the process or when the standard deviation changes. Therefore, we also proposed the GR EWMA t scheme for surveilling the mean of a process. We demonstrate that this t scheme possesses the required robust characteristic. We showcase our developed schemes' superiority over existing schemes in a detailed performance comparison. An illustrative example related to the hard-baking process is utilised to demonstrate the applicability of the suggested schemes.