ENBIS-17 in Naples

9 – 14 September 2017; Naples (Italy) Abstract submission: 21 November 2016 – 10 May 2017

Cost-Optimal Control Charts for Health-Care Data

11 September 2017, 16:00 – 16:20

Abstract

Submitted by
András Zempléni
Authors
András Zempléni (Department of Probability Theory and Statistics, Eötvös Loránd University, Budapest), Balázs Dobi (Department of Probability Theory and Statistics, Eötvös Loránd University, Budapest)
Abstract
In an earlier paper Zempléni et al (2004) introduced a Markov chain-based method for optimal design of Shewhart-type control charts, based on the economic calculations, which originate from Duncan (1974).

Control charts are traditionally used in industrial statistics. In this presentation we present a new approach, which is suitable for applications in the health care sector. Here most of the papers use standard process control charts for quality assurance (see e.g. Duclos et al., 2009). We adapt the Markov chain-based approach of Zempléni et al (2004) and develop a method, which suits for the real-life medical applications, where 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 treatment too. This means that we do not use the often-present assumption of perfect repair which is usually not realistic in case of medical treatments. The average cost of the optimal protocol, which consists of the average sampling frequency and control limits can be estimated by the stationary distribution of the Markov chain. We illustrate the approach by simulated data, based on real-life medical protocols and observations.

References:
A.J. Duncan (1974): Quality Control and Industrial Statistics (4th edn). Homewood: Illinois.
A. Duclos, S. Touzet, P. Soardo, C. Colin, J. L. Peix and J. C. Lifante (2009): Quality monitoring in thyroid surgery using the Shewhart
control chart, British Journal of Surgery, 96: 171–174.
A. Zempléni, M. Véber, B. Duarte and P. Saraiva (2004): Control charts: a cost-optimization approach for processes
with random shifts. Applied Stochastic Models in Business and Industry, 20: 185–200.

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