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

TL;DR

This paper derives a closed-form formula for the moments of mixture distributions used in control charts, aiding in optimizing parameters for healthcare process monitoring.

Contribution

It introduces a closed formula for the expected squared deviation in mixture distribution-based control charts, facilitating cost-effective healthcare process control.

Findings

Closed-form formula for moments of mixture distributions

Application to optimize control chart parameters

Enhanced control chart performance in healthcare settings

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.