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Controlling Bivariate Categorical Processes using Scan Rules

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Abstract

In this paper, we introduce a methodology for efficiently monitoring a health process that classify the intervention outcome, in two dependent characteristics, as “absolutely successful”, “with minor but acceptable complications” and “unsuccessful due to severe complications”. The monitoring procedure is based on appropriate 2-dimensional scan rules. The run length distribution is acquired by studying the waiting time distribution for the first occurrence of a 2-dimensional scan in a bivariate sequence of trinomial trials. The waiting time distribution is derived through a Markov chain embedding technique. The proposed procedure is applied on two simulated cases while it is tested against a competing method showing an excellent performance.

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Authors and Affiliations

  1. Department of Statistics & Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str., 185 34, Piraeus, Greece

    Sotirios Bersimis & Athanasios Sachlas

  2. LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597, 2 avenue du Professeur Jean Rouxel, BP 539, Cedex, 44475, Carquefou, France

    Philippe Castagliola

Authors
  1. Sotirios Bersimis
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  2. Athanasios Sachlas
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  3. Philippe Castagliola
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Correspondence to Sotirios Bersimis.

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Bersimis, S., Sachlas, A. & Castagliola, P. Controlling Bivariate Categorical Processes using Scan Rules. Methodol Comput Appl Probab 19, 1135–1149 (2017). https://doi.org/10.1007/s11009-016-9508-5

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  • DOI: https://doi.org/10.1007/s11009-016-9508-5

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