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Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval

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  • Lee, Pei-Hsi

Abstract

A combination of double sampling and variable sampling interval (DSVSI) charts can increase the efficiency of signaling small shifts. This study proposes joint DSVSI X¯ and s charts and investigates their statistical performance. The proposed approach uses a Markov chain approach to compute the statistical performance, and uses a statistical design model to design DSVSI X¯ and s charts for detecting the mean shift and variance increase. A comparison study shows that the DSVSI X¯ and s charts are better able to signal the shifts of both mean and variance than joint double sampling X¯ and s chart, adaptive X¯ and R charts, EWMA, and CUSUM charts.

Suggested Citation

  • Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
    • Handle: RePEc:eee:ejores:v:225:y:2013:i:2:p:285-297
    DOI: 10.1016/j.ejor.2012.08.020
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    References listed on IDEAS

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    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. Yongzhong Zhu & Wei Jiang, 2009. "An adaptive chart for multivariate process monitoring and diagnosis," IISE Transactions, Taylor & Francis Journals, vol. 41(11), pages 1007-1018.
    3. Yu-Chang Lin & Chao-Yu Chou, 2011. "Robustness of the EWMA and the combined X¯ --EWMA control charts with variable sampling intervals to non-normality," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(3), pages 553-570, November.
    4. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    5. Wu, Zhang & Yang, Mei & Khoo, Michael B.C. & Yu, Fong-Jung, 2010. "Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance," European Journal of Operational Research, Elsevier, vol. 205(1), pages 136-150, August.
    6. Torng, Chau-Chen & Lee, Pei-Hsi & Liao, Nai-Yi, 2009. "An economic-statistical design of double sampling control chart," International Journal of Production Economics, Elsevier, vol. 120(2), pages 495-500, August.
    7. Lin, Yu-Chang & Chou, Chao-Yu, 2007. "Non-normality and the variable parameters control charts," European Journal of Operational Research, Elsevier, vol. 176(1), pages 361-373, January.
    8. Maravelakis, Petros E. & Castagliola, Philippe, 2009. "An EWMA chart for monitoring the process standard deviation when parameters are estimated," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2653-2664, May.
    9. Pei-Hsi Lee & Chau-Chen Torng & Jhih-Cyuan Wu & Chun-Chieh Tseng, 2010. "The effectiveness study of Double Sampling s charts application on destructive testing process," International Journal of Product Development, Inderscience Enterprises Ltd, vol. 12(3/4), pages 324-335.
    10. He, David & Grigoryan, Arsen, 2006. "Joint statistical design of double sampling and s charts," European Journal of Operational Research, Elsevier, vol. 168(1), pages 122-142, January.
    11. Lee, Pei-Hsi & Torng, Chau-Chen & Liao, Li-Fang, 2012. "An economic design of combined double sampling and variable sampling interval X¯ control chart," International Journal of Production Economics, Elsevier, vol. 138(1), pages 102-106.
    12. Lee, Pei-Hsi, 2011. "Adaptive R charts with variable parameters," Computational Statistics & Data Analysis, Elsevier, vol. 55(5), pages 2003-2010, May.
    13. Wu, Zhang & Yang, Mei & Jiang, Wei & Khoo, Michael B.C., 2008. "Optimization designs of the combined Shewhart-CUSUM control charts," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 496-506, December.
    14. Chi-Shuan Liu & Fang-Chih Tien, 2011. "A single-featured EWMA- X control chart for detecting shifts in process mean and standard deviation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2575-2596, January.
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    Cited by:

    1. Song, Zhi & Mukherjee, Amitava & Liu, Yanchun & Zhang, Jiujun, 2019. "Optimizing joint location-scale monitoring – An adaptive distribution-free approach with minimal loss of information," European Journal of Operational Research, Elsevier, vol. 274(3), pages 1019-1036.
    2. Haridy, Salah & Wu, Zhang & Lee, Ka Man & Bhuiyan, Nadia, 2013. "Optimal average sample number of the SPRT chart for monitoring fraction nonconforming," European Journal of Operational Research, Elsevier, vol. 229(2), pages 411-421.
    3. Yeong, Wai Chung & Khoo, Michael B.C. & Lee, Ming Ha & Rahim, M.A., 2013. "Economic and economic statistical designs of the synthetic X¯ chart using loss functions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 571-581.
    4. Mukherjee, Amitava & Sen, Rudra, 2018. "Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality," European Journal of Operational Research, Elsevier, vol. 266(1), pages 147-167.

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