title: Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data.
abstract: In this work, we study upper-sided cumulative sum control charts that are suitable for monitoring geometrically inflated Poisson processes. We assume that a process is properly described by a two-parameter extension of the zero-inflated Poisson distribution, which can be used for modeling count data with an excessive number of zero and non-zero values. Two different upper-sided cumulative sum-type schemes are considered, both suitable for the detection of increasing shifts in the average of the process. Aspects of their statistical design are discussed and their performance is compared under various out-of-control situations. Changes in both parameters of the process are considered. Finally, the monitoring of the monthly cases of poliomyelitis in the USA is given as an illustrative example.
authors.affiliation: 1 LUNAM Université, Université de Nantes & IRCCyN UMR CNRS, Nantes, France.
authors.forename: Athanasios C
authors.initials: AC
authors.lastname: Rakitzis
authors.affiliation: 1 LUNAM Université, Université de Nantes & IRCCyN UMR CNRS, Nantes, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Castagliola
authors.affiliation: 2 Department of Business Administration, University of Piraeus, Piraeus, Greece.
authors.forename: Petros E
authors.initials: PE
authors.lastname: Maravelakis
mesh_terms: D056808:Biostatistics; D003141:Communicable Diseases / Q000453:epidemiology*; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D015233:Models, Statistical; D016012:Poisson Distribution; D011051:Poliomyelitis / Q000453:epidemiology; D011336:Probability; D062486:Public Health Surveillance; D014481:United States / Q000453:epidemiology
keywords: Average run length; Markov chain; Poisson distribution; cumulative sum control charts; inflated distribution; likelihood ratio; public-health surveillance; standard deviation of run length; statistical process control