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Simultaneous Surveillance of Means and Covariances of Spatial Models

  • Robert Garthoff
  • Philipp OttoEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 122)

Abstract

This paper deals with the problem of statistical process control applied to multivariate spatial models. After introducing the target process that coincides with the spatial white noise, we concentrate on the out-of-control behavior taking into account both changes in means and covariances. Moreover, we propose conventional multivariate control charts either based on exponential smoothing or cumulative sums to monitor means and covariances simultaneously. Via Monte Carlo simulation the proposed control schemes are calibrated. Moreover, their out-of-control behavior is studied for specific mean shifts and scale transformation.

Keywords

Control Chart Spatial Model Statistical Process Control Target Process CUSUM Chart 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Anselin L (1988) Spatial econometrics: methods and models, vol 1. Kluwer Academic, Dordrecht CrossRefGoogle Scholar
  2. 2.
    Besag J (1974) Spatial interaction and the statistical analysis of lattice systems (with discussion). J R Stat Soc B 36:192–236 MathSciNetGoogle Scholar
  3. 3.
    Cliff AD, Ord JK (1973) Spatial autocorrelation. Pion, London Google Scholar
  4. 4.
    Cliff AD, Ord JK (1981) Spatial processes: models & applications, vol 44. Pion, London zbMATHGoogle Scholar
  5. 5.
    Cressie N (1993) Statistics for spatial data. Wiley, New York Google Scholar
  6. 6.
    Crosier R (1988) Multivariate generalizations of cumulative sum quality control schemes. Technometrics 30:291–303 MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Garthoff R, Otto P (2014) Control charts for multivariate spatial autoregressive models. European University Viadrina. Department of Business Administration and Economics. Discussion Paper Google Scholar
  8. 8.
    Golosnoy V, Ragulin S, Schmid W (2009) Multivariate CUSUM chart: properties and enhancements. AStA Adv Stat Anal 93:263–279 MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hotelling H (1947) Multivariate quality control. In: Eisenhart C, Hastay MW, Wallis MA (eds) Techniques of statistical analysis. McGraw–Hill, New York Google Scholar
  10. 10.
    Lowry C, Woodall W, Champ C, Rigdon S (1992) A multivariate exponentially weighted moving average control chart. Technometrics 34:46–53 CrossRefzbMATHGoogle Scholar
  11. 11.
    Ngai H-M, Zhang J (2001) Multivariate cumulative sum control charts based on projection pursuit. Stat Sin 11:747–766 MathSciNetzbMATHGoogle Scholar
  12. 12.
    Ord JK (1975) Estimation methods for models of spatial interaction. J Am Stat Assoc 70(349):120–126 MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Pignatiello J, Runger G (1990) Comparison of multivariate CUSUM charts. J Qual Technol 22:173–186 Google Scholar
  14. 14.
    Śliwa P, Schmid W (2005) Monitoring the cross-covariances of a multivariate time series. Metrika 61:89–115 MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Śliwa P, Schmid W (2005) Surveillance of the covariance matrix of multivariate nonlinear time series. Statistics 39:221–246 MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Whittle P (1954) On stationary processes in the plane. Biometrika 41:434–449 MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.European University ViadrinaFrankfurt (Oder)Germany

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