Control charts for skewed distributions

Abstract

In this paper the control limits of \(\bar{X}\) and \(R\) control charts for skewed distributions are obtained by considering the classic, the weighted variance (\(\mathit{WV}\)), the weighted standard deviations (\(\mathit{WSD}\)) and the skewness correction (\(\mathit{SC}\)) methods. These methods are compared by using Monte Carlo simulation. Type I risk probabilities of these control charts are compared with respect to different subgroup sizes for skewed distributions which are Weibull, gamma and lognormal. Simulation results show that Type I risk of \(\mathit{SC}\) method is less than that of other methods. When the distribution is approximately symmetric, then the Type I risks of Shewhart, \(\mathit{WV}\) , \(\mathit{WSD}\), and \(\mathit{SC}\) \(\bar{X}\) charts are comparable, while the \(\mathit{SC}\) \(R\) chart has a noticeable smaller Type I risk.