X bar control chart for non-normal symmetric distributions

Abstract

In statistical quality control, X bar control chart is extensively used to monitor a change in the process mean. In this paper, X bar control chart for non-normal symmetric distributions is proposed. For chosen Student, Laplace, logistic and uniform distributions of quality characteristic, we calculated theoretical distribution of standardized sample mean and fitted Pearson type II or type VII distributions. Width of control limits and power of the X bar control chart were established, giving evidence of the goodness of fit of the corresponding Pearson distribution to the theoretical distribution of standardized sample mean. For implementation of X bar control chart in practice, numerical example of construction of a proposed chart is given.