A Note on the Moments of Special Mixture Distributions, with Applications for Control Charts

Abstract: Control charts can be applied in a wide range of areas, this paper focuses on generalisations suitable for healthcare applications. We concentrate on the effect of using mixture distributions as the possible shifts in the process mean value. We give a closed formula for the expected squared deviation from the target value between samplings. This observation can be utilised in finding the cost-optimal parameters of the control chart.