Control charts for positively‐skewed populations with weighted standard deviations

This paper proposes a heuristic method of constructing $\bar{X}$ , cumulative sum and exponentially weighted moving average control charts for skewed populations with weighted standard deviations obtained by decomposing the standard deviation into upper and lower deviations adjusted in accordance with the direction and degree of skewness. These control charts, however, reduce to standard control charts when the underlying distribution is symmetric. Simple formulae are derived to estimate unknown process parameters from means and ranges of subgroups. The false alarm rates of these control charts are compared with those of existing control charts when the underlying distribution is Weibull, gamma, or lognormal. Simulation results show that considerable improvement over the existing methods can be achieved when the underlying distribution is skewed. Copyright © 2001 John Wiley & Sons, Ltd.