The joint economic-statistical design of (X)over-bar and R control charts for nonnormal data

We consider the joint economic-statistical design of X and R control charts, assuming that the quality measurement and the in-control time have Johnson and Weibull distributions, respectively. The Johnson distribution is general in that it can be made to fit all possible values of skewness and kurtosis. The four parameters-the sample size, time between successive samples, and the control factors for X and R charts-are determined so that the expected hourly cost is minimized under constrains on Type I and II error probabilities. Our cost model is an extension of the Costa model to include the Johnson and Weibull assumptions. Sensitivity to nonnormality, Weibull shape, and shift are considered. The sensitivity analysis shows that the optimal design parameters are sensitive to nonnormality.