An evolutionary economic-statistical design for VSI X control charts under non-normality

Since Reynolds et al. [1] proposed the variable sampling interval (VSI) (X) over bar control chart, the statistical properties of the chart have been discussed and shown to be better than the traditional control chart in which the sampling intervals length are fixed. However, the VSI charts are, like the traditional charts, still costly when they are used for the prevention of defective products. For this reason, an appropriate design is necessary before it is used. In this paper, a VSI (X) over bar control chart is used for monitoring non-normal process data, which is widely encountered in practice. Then, a cost-quality model based on the Burr distribution is proposed for constructing an economic-statistical design for the VSI (X) over bar chart. The design of the chart has been developed considering the optimisation of the cost function in this model posed by statistical constraints. The design parameters can be derived through the evolutionary search method, and the overall finding indicates that the designed VSI chart always outperforms the traditional control chart with respect to the expected cost per unit time. This model is also suitable for normally distributed data; thus, it is suitable for a general application.