Exponentially weighed moving average charts for monitoring zero-inflated proportions with applications in health care

Abstract

In the context of public health surveillance, the aim is to monitor the occurrence of health-related events. Among them, statistical process monitoring focuses very often on the monitoring of rates and proportions (i.e. values in $(0,1)$ ) such as the proportion of patients with a specific disease. A popular control chart that is able to detect quickly small to moderate shifts in process parameters is the exponentially weighed moving average control chart. There are various models that are used to describe values in $(0,1)$ . However, especially in the case of rare health events, zero values occur very frequently which, for example, denote the absence of the disease. In this paper, we study the performance and the statistical design of exponentially weighed moving average control charts for monitoring proportions that arise in a health-related framework. The proposed chart is based on the zero-inflated Beta distribution, a mixed (discrete-continuous) distribution, suitable for modelling data in $[0,1)$ . We use a Markov chain method to study the run length distribution of the exponentially weighed moving average chart. Also, we investigate the statistical design as well as the performance of the proposed charts. Comparisons with a Shewhart-type chart are also given. Finally, we provide an example for the practical implementation of the proposed charts.