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Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length

Author

Listed:
  • Moi Hua Tuh

    (Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Cawangan Sarawak, Kota Samarahan 94300, Sarawak, Malaysia
    Faculty of Engineering, Computing and Science, Swinburne University of Technology Sarawak Campus, Kuching 93350, Sarawak, Malaysia)

  • Cynthia Mui Lian Kon

    (Faculty of Engineering, Computing and Science, Swinburne University of Technology Sarawak Campus, Kuching 93350, Sarawak, Malaysia)

  • Hong Siang Chua

    (Faculty of Engineering, Computing and Science, Swinburne University of Technology Sarawak Campus, Kuching 93350, Sarawak, Malaysia)

  • Man Fai Lau

    (School of Software and Electrical Engineering, Swinburne University of Technology, Melbourne, VIC 3122, Australia)

  • Yee Hui Robin Chang

    (Faculty of Applied Sciences, Universiti Teknologi MARA, Cawangan Sarawak, Kota Samarahan 94300, Sarawak, Malaysia)

Abstract

To keep an eye on the status of high-quality processes for fraction nonconforming, the synthetic double sampling (SDS) np chart is a helpful tool. The SDS np chart is a hybrid between the double sampling (DS) np chart and the conforming run length (CRL) chart. The performance of a control chart is typically judged solely using the average run length (ARL). However, as the shape of the run length (RL) distribution varies with the magnitude of the shift in the process fraction nonconforming, the ARL no longer provides clear interpretation of a chart’s performance. Subsequently, enhanced DS np charts that use median run length (MRL) and expected median run length (EMRL) measures, including SDS np with MRL have recently been proposed for addressing this setback. To broaden the functionality of SDS np , in this work, the unexplored use of EMRL as alternative performance measure is developed by means of Markov chain model. Additionally, in both the zero-state (ZS) and steady-state (SS) modes, the novel optimal designs algorithms are described for computing the optimal charting parameters of the SDS np chart, for both MRL 1 and EMRL 1 minimizations, without any unfavourable feature of bilateral sensitivity. Both the MRL and EMRL performances of SDS np , synthetic np , and DS np charts are compared. Optimal designs charting parameters and sensitivity analyses are provided to aid the practical application of SDS np chart.

Suggested Citation

  • Moi Hua Tuh & Cynthia Mui Lian Kon & Hong Siang Chua & Man Fai Lau & Yee Hui Robin Chang, 2023. "Evaluating the Performance of Synthetic Double Sampling np Chart Based on Expected Median Run Length," Mathematics, MDPI, vol. 11(3), pages 1-23, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:595-:d:1044721
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    References listed on IDEAS

    as
    1. Michael Khoo & How Lee & Zhang Wu & Chung-Ho Chen & Philippe Castagliola, 2010. "A synthetic double sampling control chart for the process mean," IISE Transactions, Taylor & Francis Journals, vol. 43(1), pages 23-38.
    2. H.W. You & Michael B.C. Khoo & P. Castagliola & Liang Qu, 2016. "Optimal exponentially weighted moving average charts with estimated parameters based on median run length and expected median run length," International Journal of Production Research, Taylor & Francis Journals, vol. 54(17), pages 5073-5094, September.
    3. Michael Khoo & V. Wong & Zhang Wu & Philippe Castagliola, 2012. "Optimal design of the synthetic chart for the process mean based on median run length," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 765-779.
    4. Huay Woon You, 2018. "Performance of Synthetic Double Sampling Chart with Estimated Parameters Based on Expected Average Run Length," Journal of Probability and Statistics, Hindawi, vol. 2018, pages 1-6, May.
    5. 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.
    6. Aurelia De Araujo Rodrigues & Eugenio Kahn Epprecht & Maysa Sacramento De Magalhaes, 2011. "Double-sampling control charts for attributes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(1), pages 87-112.
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