The Economic and Economic-Statistical Designs of the Synthetic Chart for the Coefficient of Variation

Control charts are one of the tools used to monitor processes based on statistical principles. Standard control charts in the literature mostly monitor changes in the mean, the standard deviation, or both. However, these charts provide dubious results when the mean is not constant and the standard deviation changes with the mean. For such processes, monitoring the coefficient of variation (CV) is a better approach. In the literature, very few studies are available on the economic and economic-statistical designs of the CV charts. This makes it difficult for practitioners who wish to implement CV charts at an economically optimal level. Thus, this paper filled the gap in research by proposing economic and economic-statistical designs for the synthetic CV chart. As it is often difficult to estimate the shift size, the designs proposed in this paper considered both the known and unknown shift size cases. For the known shift size case, the shift size needed to be specified as an exact value, while for the unknown shift size case, the shift size only needed to be specified as a range of possible values. Subsequently, a sensitivity analysis was performed to investigate the effects of different input parameters. The effects of statistical constraints and the effects of incorrect specification of the shift size were also studied. When there is uncertainty regarding the shift size, guidelines are proposed to select an appropriate range for it. Finally, comparisons were made between the synthetic, Shewhart, exponentially weighted moving average (EWMA), and cumulative sum (CUSUM) CV charts. Comparisons were also made between the zero-state, conditional steady-state, and cyclical steady-state synthetic CV charts.