Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts

  • Kim Phuc Tran
  • Philippe Castagliola
  • Giovanni Celano
Regular Article


Continuous surveillance of the ratio of population means of bivariate normal distributions is a quality control issue worth of consideration in several manufacturing and service-oriented companies. For this reason, some recent studies have investigated traditional and advanced Shewhart control charts to perform on-line monitoring of this kind of ratio. Anyway, Shewhart control charts are known to be insensitive to small and moderate shift sizes. Up to now, CUSUM control charts have not yet been considered for this quality control problem. In this paper, we propose and investigate the statistical properties of two Phase II one-sided CUSUM control charts for monitoring the ratio of population means of a bivariate normal distribution. Several figures and tables are provided to show the sensitivity of the two CUSUM charts to different deterministic shift sizes and their performance for the random shift size condition. In most cases, the numerical results demonstrate that the proposed CUSUM control charts are very sensitive to shifts in the ratio. An illustrative example comments the use of these charts in a simulated quality control problem from the food industry.


Ratio distribution Markov chain CUSUM 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Kim Phuc Tran
    • 1
  • Philippe Castagliola
    • 1
  • Giovanni Celano
    • 2
  1. 1.LUNAM Université, Université de Nantes & IRCCyN UMR CNRS 6597NantesFrance
  2. 2.Department of Civil Engineering and ArchitectureUniversity of CataniaCataniaItaly

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