  Control charts have traditionally been used in industrial statistics, but are
constantly seeing new areas of application, especially in the age of Industry
4.0. This paper introduces a new method, which is suitable for applications in
the healthcare sector, especially for monitoring a health-characteristic of a
patient. We adapt a Markov chain-based approach and develop a method in which
not only the shift size (i.e. the degradation of the patient's health) can be
random, but the effect of the repair (i.e. treatment) and time between
samplings (i.e. visits) too. This means that we do not use many often-present
assumptions which are usually not applicable for medical treatments. The
average cost of the protocol, which is determined by the time between samplings
and the control limit, can be estimated using the stationary distribution of
the Markov chain.
  Furthermore, we incorporate the standard deviation of the cost into the
optimisation procedure, which is often very important from a process control
viewpoint. The sensitivity of the optimal parameters and the resulting average
cost and cost standard deviation on different parameter values is investigated.
We demonstrate the usefulness of the approach for real-life data of patients
treated in Hungary: namely the monitoring of cholesterol level of patients with
cardiovascular event risk. The results showed that the optimal parameters from
our approach can be somewhat different from the original medical parameters.

Applications;Computers and Society;Methodology;Machine Learning