The x-bar control chart under non-normality

This paper studies design schemes for the control chart under non-normality. Different estimators of the standard deviation are considered and the effect of the estimator on the performance of the control chart under non-normality is investigated. Two situations are distinguished. In the first situation, the effect of non-normality on the control chart is investigated by using the control limits based on normality. In the second situation we incorporate the knowledge of non-normality to correct the limits of the control chart. The schemes are evaluated by studying the characteristics of the in-control and the out-of-control run length distributions. The results indicate that when the control limits based on normality are applied the best estimator is the pooled sample standard deviation both under normality and under non-normality. When the control limits are corrected for non-normality, the estimator based on Gini's mean sample differences is the best choice.