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

Wenpo Huang, Lianjie Shu, Wei Jiang and Kwok-Leung Tsui

IISE Transactions, 2013, vol. 45, issue 9, 981-994

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.

Date: 2013
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DOI: 10.1080/0740817X.2012.705455

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