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The exponentiated exponentially weighted moving average control chart

Author

Listed:
  • Vasileios Alevizakos

    (National Technical University of Athens)

  • Arpita Chatterjee

    (Georgia Southern University)

  • Kashinath Chatterjee

    (Augusta University)

  • Christos Koukouvinos

    (National Technical University of Athens)

Abstract

Memory-type control charts are widely used for monitoring small to moderate shifts in the process parameter(s). In the present article, we present an exponentiated exponentially weighted moving average (Exp-EWMA) control chart that weights the past observations of a process using an exponentiated function. We evaluated the run-length characteristics of the Exp-EWMA chart via Monte Carlo simulations. A comparison study versus the CUSUM, EWMA and extended EWMA (EEWMA) charts under similar in-control (IC) run-length properties demonstrates that the Exp-EWMA chart is more effective for detecting small and, under certain circumstances, moderate shifts for both the zero-state and steady-state cases. Moreover, the Exp-EWMA chart has better zero-state out-of-control (OOC) performance than an EWMA chart with smoothing parameter equal to the limit to the infinity of the exponentiated function, while the two charts perform similarly for the steady-state case. Finally, it is shown that the Exp-EWMA chart is more IC robust than its competitors under several non-normal distributions. Two examples are provided to explain the implementation of the proposed chart

Suggested Citation

  • Vasileios Alevizakos & Arpita Chatterjee & Kashinath Chatterjee & Christos Koukouvinos, 2024. "The exponentiated exponentially weighted moving average control chart," Statistical Papers, Springer, vol. 65(6), pages 3853-3891, August.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:6:d:10.1007_s00362-024-01544-2
    DOI: 10.1007/s00362-024-01544-2
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    References listed on IDEAS

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    1. Sven Knoth, 2015. "Run length quantiles of EWMA control charts monitoring normal mean or/and variance," International Journal of Production Research, Taylor & Francis Journals, vol. 53(15), pages 4629-4647, August.
    2. Nasir Abbas & Muhammad Riaz & Ronald J. M. M. Does, 2014. "An EWMA-Type Control Chart for Monitoring the Process Mean Using Auxiliary Information," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(16), pages 3485-3498, August.
    3. Seven Knoth, 2005. "Fast initial response features for EWMA control charts," Statistical Papers, Springer, vol. 46(1), pages 47-64, January.
    4. YuLong Qiao & JinSheng Sun & Philippe Castagliola & XueLong Hu, 2022. "Optimal design of one-sided exponential EWMA charts based on median run length and expected median run length," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(9), pages 2887-2907, March.
    5. Muhammad Shujaat Nawaz & Muhammad Azam & Muhammad Aslam, 2021. "EWMA and DEWMA repetitive control charts under non-normal processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(1), pages 4-40, January.
    6. S. W. Human & P. Kritzinger & S. Chakraborti, 2011. "Robustness of the EWMA control chart for individual observations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(10), pages 2071-2087.
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