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Evaluation of run-length distribution for CUSUM charts under gamma distributions

Author

Listed:
  • Wenpo Huang
  • Lianjie Shu
  • Wei Jiang
  • Kwok-Leung Tsui

Abstract

Numerical evaluation of run-length distributions of CUSUM charts under normal distributions has received considerable attention. However, accurate approximation of run-length distributions under non-normal or skewed distributions is challenging and has generally been overlooked. This article provides a fast and accurate algorithm based on the piecewise collocation method for computing the run-length distribution of CUSUM charts under skewed distributions such as gamma distributions. It is shown that the piecewise collocation method can provide a more robust approximation of the run-length distribution than other existing methods such as the Gaussian quadrature-based approach, especially when the process distribution is heavily skewed. Some computational aspects including an alternative formulation based on matrix decomposition and geometric approximation of run-length distribution are discussed. Design guidelines of such a CUSUM chart are also provided.

Suggested Citation

  • Wenpo Huang & Lianjie Shu & Wei Jiang & Kwok-Leung Tsui, 2013. "Evaluation of run-length distribution for CUSUM charts under gamma distributions," IISE Transactions, Taylor & Francis Journals, vol. 45(9), pages 981-994.
    • Handle: RePEc:taf:uiiexx:v:45:y:2013:i:9:p:981-994
    DOI: 10.1080/0740817X.2012.705455
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    Cited by:

    1. Lianjie Shu & Wenpo Huang & Wei Jiang, 2014. "A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(3), pages 223-237, April.

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