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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

15 Scopus Citations
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Author(s)

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

Detail(s)

Original languageEnglish
Pages (from-to)981-994
Journal / PublicationIIE Transactions (Institute of Industrial Engineers)
Volume45
Issue number9
Publication statusPublished - 1 Sep 2013

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. © 2013 Taylor & Francis Group, LLC.

Research Area(s)

  • Average run length, integral equation, skewed distributions, statistical process control, variance

Citation Format(s)

Evaluation of run-length distribution for CUSUM charts under gamma distributions. / Huang, Wenpo; Shu, Lianjie; Jiang, Wei; Tsui, Kwok-Leung.

In: IIE Transactions (Institute of Industrial Engineers), Vol. 45, No. 9, 01.09.2013, p. 981-994.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review