Effects of misspecification on the economic-statistical design of the Coefficient Of Variation chart

The Coefficient of Variation (CV) chart monitors changes in the ratio of the standard deviation against the mean, instead of monitoring changes in the mean and/or standard deviation. The economic-statistical design of the CV chart allows practitioners to select optimal chart parameters which minimize the cost subject to constraints in the run length. However, a large number of parameters need to be estimated. This study looks at the effects when these parameters are incorrectly estimated. It was found that a minimal increase in cost is shown when the parameters are not estimated accurately, except for the incorrect specification of the shift size and the out-of-control quality cost which shows a slightly higher increase in cost. Thus, only a rough approximation is needed for most of the parameters.