Control charts for positively-skewed populations with weighted standard deviations

This paper proposes a heuristic method of constructing X, cumulative sum an d exponentially weighted moving average control charts for skewed populatio ns with weighted standard deviations obtained by decomposing the standard d eviation into upper and lower deviations adjusted in accordance with the di rection and degree of skewness. These control charts, however, reduce to st andard 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 com pared with those of existing control charts when the underlying distributio n is Weibull, gamma, or lognormal. Simulation results show that considerabl e improvement over the existing methods can be achieved when the underlying distribution is skewed. Copyright (C) 2001 John Wiley & Sons, Ltd.