Optimal design of second-order linear filters for control charting

Chang Ho Chin*, Daniel W. Apley

*Corresponding author for this work

Research output: Contribution to specialist publicationArticle

12 Scopus citations


In many common control charting situations, the statistic to be charted can be viewed as the output of a linear filter applied to the sequence of process measurement data. In recent work that has generalized this concept, the charted statistic is the output of a general linear filter in impulse response form, and the filter is designed by selecting its impulse response coefficients to optimize its average run length performance. In this work, we restrict attention to the class of all second-order linear filters applied to the residuals of a time series model of the process data. We present an algorithm for optimizing the design of the second-order filter that is more computationally efficient and robust than the algorithm for optimizing the general linear filter. We demonstrate that the optimal second-order filter performs almost as well as the optimal general linear filter in many situations. Both methods share a number of interesting characteristics and are tuned to detect any distinct features of the process mean shift as it manifests itself in the residuals.

Original languageEnglish (US)
Number of pages12
Specialist publicationTechnometrics
StatePublished - Aug 2006


  • Autocorrelation
  • Control chart
  • Linear filtering
  • Markov chain method
  • Statistical process control
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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