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An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process

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  • Chia-Ding Hou

    (Department of Statistics and Information Science, Fu Jen Catholic University, New Taipei City 242062, Taiwan)

  • Rung-Hung Su

    (Department of Statistics and Information Science, Fu Jen Catholic University, New Taipei City 242062, Taiwan)

Abstract

Among attribute processes, the number of nonconformities conforming to a Poisson distribution is among the most crucial quality attributes. Furthermore, owing to the variety of quality attributes, the significance of the multivariate Poisson process in industry cannot be overstated. An out-of-control multivariate Poisson process can be detected using an alarm on a multivariate control chart. Nevertheless, pinpointing the specific quality attributes that led to the process shifts is complex. The study focuses on the causes that lead to process shifts in multivariate Poisson processes, unlike the majority of studies examining shifts in multivariate normal processes. This paper initially presents a statistical method for detecting outliers in a multivariate Poisson distribution. Furthermore, a progressive testing algorithm is then developed to identify the variables responsible for a failure within a multivariate Poisson process. According to simulation results, the proposed approach can effectively determine the sources of a process fault within a multivariate Poisson process.

Suggested Citation

  • Chia-Ding Hou & Rung-Hung Su, 2024. "An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process," Mathematics, MDPI, vol. 12(18), pages 1-10, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:18:p:2813-:d:1475904
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    References listed on IDEAS

    as
    1. Chia-Ding Hou & Jengtung Chiang & John Jen Tai, 2001. "Identifying Chromosomal Fragile Sites from a Hierarchical-Clustering Point of View," Biometrics, The International Biometric Society, vol. 57(2), pages 435-440, June.
    2. Yuehjen E. Shao & Chi-Jie Lu & Yu-Chiun Wang, 2012. "A Hybrid ICA-SVM Approach for Determining the Quality Variables at Fault in a Multivariate Process," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-12, September.
    3. Jinho Kim & Myong K. Jeong & Elsayed A. Elsayed & K.N. Al-Khalifa & A.M.S. Hamouda, 2016. "An adaptive step-down procedure for fault variable identification," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3187-3200, June.
    4. Yuehjen E. Shao & Chia-Ding Hou, 2013. "Fault Identification in Industrial Processes Using an Integrated Approach of Neural Network and Analysis of Variance," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, June.
    5. Yuehjen E. Shao, 2014. "Recognition of Process Disturbances for an SPC/EPC Stochastic System Using Support Vector Machine and Artificial Neural Network Approaches," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, June.
    6. Hamed Sabahno & Seyed Taghi Akhavan Niaki, 2023. "New Machine-Learning Control Charts for Simultaneous Monitoring of Multivariate Normal Process Parameters with Detection and Identification," Mathematics, MDPI, vol. 11(16), pages 1-31, August.
    7. Hongying Jing & Jian Li & Kaizong Bai, 2022. "Directional monitoring and diagnosis for covariance matrices," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(6), pages 1449-1464, April.
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