The economic and economic-statistical designs of the coefficient of variation chart

Superior quality of manufactured products ensures sustainability in industries. However, the cost of monitoring and improving quality can be high. To overcome the high cost of quality control, this paper proposes economic and economic-statistical designs of the coefficient of variation (CV) chart. The CV chart monitors the ratio of the standard deviation to the mean, and is useful in processes where the mean is not constant and/or the variance is a function of the mean. In these processes, the traditional Xbar and S or R charts cannot be used. Although many studies are done on the CV chart, an economic model which minimizes the cost of implementing the CV chart cannot be found in the existing literature. Thus, this paper proposes a simplified algorithm to obtain the optimal chart parameters of the CV chart, i.e. the sample size, the sampling interval, the upper control limit and the lower control limit, which minimize the expected cost function. Two models are considered. In the economic design, the expected cost function is minimized without the need to satisfy statistical constraints; while for the economic statistical design, the expected cost function is minimized subject to statistical constraints. A sensitivity analysis to identify the input parameters which have a significant impact on the cost and choice of optimal chart’s parameters of the CV chart are performed based on numerical examples. Besides that, the effects of adding statistical constraints are investigated.