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Sequential monitoring of a Bernoulli sequence when the pre-change parameter is unknown

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  • Gordon Ross
  • Dimitris Tasoulis
  • Niall Adams

Abstract

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world situations: (1) the pre-change value of the Bernoulli parameter is known in advance, (2) computational efficiency is not paramount, and (3) enough observations occur between change points to allow asymptotic approximations to be used. We develop a novel change detection method based on Fisher’s exact test which does not make any of these assumptions. We show that our method can be implemented in a computationally efficient manner, and is hence suited to sequential monitoring where new observations are constantly being received over time. We assess our method’s performance empirically via using simulated data, and find that it is comparable to the optimal CUSUM scheme which assumes both pre- and post-change values of the parameter to be known. Copyright Springer-Verlag 2013

Suggested Citation

  • Gordon Ross & Dimitris Tasoulis & Niall Adams, 2013. "Sequential monitoring of a Bernoulli sequence when the pre-change parameter is unknown," Computational Statistics, Springer, vol. 28(2), pages 463-479, April.
    • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:463-479
    DOI: 10.1007/s00180-012-0311-7
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    References listed on IDEAS

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    1. Arthur B. Yeh & Richard N. Mcgrath & Mark A. Sembower & Qi Shen, 2008. "EWMA control charts for monitoring high-yield processes based on non-transformed observations," International Journal of Production Research, Taylor & Francis Journals, vol. 46(20), pages 5679-5699, January.
    2. Chunguang Zhou & Changliang Zou & Yujuan Zhang & Zhaojun Wang, 2009. "Nonparametric control chart based on change-point model," Statistical Papers, Springer, vol. 50(1), pages 13-28, January.
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    Cited by:

    1. Jorge Hernán Toro-Córdoba & Fredy Gamboa-Estrada & Laura Viviana León-Díaz & Martha López & Lucía Arango-Lozano & Diego Alejandro Martínez-Cruz & Luis Fernando Melo-Velandia & Carlos Andrés Quicazán-M, 2023. "Flujos de Capital de Portafolio en Colombia," Revista ESPE - Ensayos sobre Política Económica, Banco de la Republica de Colombia, issue 105, pages 1-103, July.

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    More about this item

    Keywords

    Binomial change detection; Process control;

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