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Control charts have traditionally been used in industrial statistics, but areconstantly seeing new areas of application, especially in the age of Industry4.0. This paper introduces a new method, which is suitable for applications inthe healthcare sector, especially for monitoring a health-characteristic of apatient. We adapt a Markov chain-based approach and develop a method in whichnot only the shift size (i.e. the degradation of the patient's health) can berandom, but the effect of the repair (i.e. treatment) and time betweensamplings (i.e. visits) too. This means that we do not use many often-presentassumptions which are usually not applicable for medical treatments. Theaverage cost of the protocol, which is determined by the time between samplingsand the control limit, can be estimated using the stationary distribution ofthe Markov chain.  Furthermore, we incorporate the standard deviation of the cost into theoptimisation procedure, which is often very important from a process controlviewpoint. The sensitivity of the optimal parameters and the resulting averagecost and cost standard deviation on different parameter values is investigated.We demonstrate the usefulness of the approach for real-life data of patientstreated in Hungary: namely the monitoring of cholesterol level of patients withcardiovascular event risk. The results showed that the optimal parameters fromour approach can be somewhat different from the original medical parameters.

Markov Chain-based Cost-Optimal Control Charts for Healthcare Data