Description
In an earlier paper Zempléni et al. (2004) introduced a Markov chain-based method for the economically optimal design of Shewhart-type control charts originating from Duncan’s cycle-based model (1956).
Control charts are traditionally used in industrial statistics. We introduce a new approach, which is suitable for applications in the healthcare sector. Most papers in this area use standard process control charts only for quality assurance (see e.g. Duclos et al., 2009). We adapt the Markov chain-based approach and develop a method in which not only the shift (i.e. the degradation of the patient’s health) can be random, but the sampling interval (i.e. time between visits) and the effect of the repair (i.e. treatment) too. This means that we do not use the often-present assumption of perfect repair which is usually not applicable for medical treatments. The average cost of the optimal protocol, which consists of the sampling frequency (i.e. optimal frequency of control visits) and control limits (i.e. optimal medical criteria) can be estimated by the stationary distribution of the Markov chain.
1. Zempléni, A., Véber, M., Duarte, B. and Saraiva, P. (2004) Control Charts: A cost-optimization approach for processes with random shifts. ASMBI, 20, p.185-200.
2. Duncan, A. J. (1956). The Economic Design of X Charts Used to Maintain Current Control of a Process. Journal of the American Statistical Association, Vol. 51
3. A. Duclos, S. Touzet, P. Soardo, C. Colin, J. L. Peix, J. C. Lifant (2009) Quality monitoring in thyroid surgery using the Shewhart control chart. British Journal of Surgery, Vol. 96, Issue 2