Evaluating the Steady-state Performance of the Synthetic Coefficient of Variation Chart

The synthetic coefficient of variation (CV) chart is attractive to practitioners as it allows for a second point to fall outside the control limits before deciding whether the process is out-of-control. The existing synthetic CV chart is designed with a head-start feature, which shows an advantage under the zero-state assumption where shifts happen immediately after process monitoring has started. However, this assumption may not be valid as shifts may happen quite some time after process monitoring has started. This is called the steady-state condition. This paper evaluates the performance of the chart under the steady-state condition. It is shown that the steady-state out-of-control average run length (ARL1) is substantially larger than the zero-state ARL1, hence larger number of samples are needed to detect the out-of-control condition. From the comparison with other CV charts, the steady-state synthetic CV chart does not show better performance, especially for small sample sizes and shift sizes. Hence, the synthetic CV chart is not recommended to be adopted under the steady-state condition, and its good performance is only applicable under the zero-state assumption. The results of this paper enable practitioners to be aware that the performance of the synthetic CV chart may be inferior under actual application (when shifts do not happen at the beginning of process monitoring) compared to its zero-state performance.