Control charts for skewed distributions : Weibull, gamma and lognormal

Abstract

In this paper the control limits of X and R control charts for skewed distributions are obtained by considering the classic, the weighted variance (WV ), the weighted standard deviations (WSD) and the skewness correction (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 SC method is less than that of other methods. When the distribution is approximately symmetric, then the type I risks of Shewhart, WV , WSD, and SC X charts are comparable, while the SC R chart has a noticeable smaller Type I risk.