Economic design of the VSSI X¯ control charts for correlated data

An X¯ chart with variable sample size and sampling interval (VSSI) has been shown superior to the traditional X¯ chart with fixed sample size and sampling interval. However, the VSSI chart is still costly when it is used for the prevention of defective products. As a result, some cost models were developed to express the long-run cost per hour of operating the VSSI chart and to gain insight into the way to design the chart parameters. An underlying assumption for these models is that the process data is independent. However, in practice there are many situations where the correlation does exist within the sample. Thus, a cost model combining Costa's cost model with the multivariate normal distribution model given by Yang and Hancock is developed in this study to explore the effect of correlation on the designed chart parameters. An evolutionary method of finding the optimal values of sample size, sampling interval length, control limit and warning limit is presented. An example is given to illustrate the model application. Sensitivity analysis on the input parameters (i.e., the cost and process parameters) of the model is also presented.