Methodology and Computing in Applied Probability

, Volume 19, Issue 4, pp 1135–1149 | Cite as

Controlling Bivariate Categorical Processes using Scan Rules

  • Sotirios BersimisEmail author
  • Athanasios Sachlas
  • Philippe Castagliola


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.


Multi-attribute processes Markov chain embeddable random variables Multivariate statistical process control Waiting time distributions 

Mathematics Subject Classification

60E05 60J10 


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Sotirios Bersimis
    • 1
    Email author
  • Athanasios Sachlas
    • 1
  • Philippe Castagliola
    • 2
  1. 1.Department of Statistics & Insurance ScienceUniversity of PiraeusPiraeusGreece
  2. 2.LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597CarquefouFrance

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