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Process Monitoring Using Truncated Gamma Distribution

Author

Listed:
  • Sajid Ali

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    These authors contributed equally to this work.)

  • Shayaan Rajput

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    These authors contributed equally to this work.)

  • Ismail Shah

    (Department of Statistics, Quaid-i-Azam University, Islamabad 45320, Pakistan
    Department of Statistical Sciences, University of Padua, 35121 Padua, Italy
    These authors contributed equally to this work.)

  • Hassan Houmani

    (Department of Economics, School of Business, Lebanese International University-LIU, Beirut 146404, Lebanon
    These authors contributed equally to this work.)

Abstract

The time-between-events idea is commonly used for monitoring high-quality processes. This study aims to monitor the increase and/or decrease in the process mean rapidly using a one-sided exponentially weighted moving average (EWMA) chart for the detection of upward or downward mean shifts using a truncated gamma distribution. The use of the truncation method helps to enhance and improve the sensitivity of the proposed chart. The performance of the proposed chart with known and estimated parameters is analyzed by using the run length properties, including the average run length (ARL) and standard deviation run length (SDRL), through extensive Monte Carlo simulation. The numerical results show that the proposed scheme is more sensitive than the existing ones. Finally, the chart is implemented in real-world situations to highlight the significance of the proposed chart.

Suggested Citation

  • Sajid Ali & Shayaan Rajput & Ismail Shah & Hassan Houmani, 2023. "Process Monitoring Using Truncated Gamma Distribution," Stats, MDPI, vol. 6(4), pages 1-25, December.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:80-1322:d:1292761
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    References listed on IDEAS

    as
    1. Wu, Zhang & Luo, Hua & Zhang, Xiaolan, 2006. "Optimal np control chart with curtailment," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1723-1741, November.
    2. Liang Qu & Michael B.C. Khoo & Philippe Castagliola & Zhen He, 2018. "Exponential cumulative sums chart for detecting shifts in time-between-events," International Journal of Production Research, Taylor & Francis Journals, vol. 56(10), pages 3683-3698, May.
    3. Shu Wu & Philippe Castagliola & Giovanni Celano, 2021. "A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(3), pages 434-454, February.
    4. Zhang Wu & Qinan Wang, 2007. "An NP Control Chart Using Double Inspections," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(7), pages 843-855.
    5. Ahtasham Gul & Muhammad Mohsin & Muhammad Adil & Mansoor Ali, 2021. "A modified truncated distribution for modeling the heavy tail, engineering and environmental sciences data," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-24, April.
    Full references (including those not matched with items on IDEAS)

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