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Optimal average sample number of the SPRT chart for monitoring fraction nonconforming

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  • Haridy, Salah
  • Wu, Zhang
  • Lee, Ka Man
  • Bhuiyan, Nadia

Abstract

The Sequential Probability Ratio Test (SPRT) control chart is a powerful tool for monitoring manufacturing processes. It is highly suitable for the applications where testing is destructive or very expensive, such as the automobile airbags test. This article studies the effect of the Average Sample Number (ASN) (i.e., the average sample size) on the chart’s performance. A design algorithm is proposed to develop the optimal SPRT chart for monitoring the fraction nonconforming p of Bernoulli processes. By optimizing the ASN and other charting parameters, the average detection speed of the SPRT chart is almost doubled. It is also found that the optimal SPRT chart significantly outperforms the optimal np and binomial CUSUM charts, in terms of Average Number of Defectives (AND), under different combinations of the design specifications. It is observed that the SPRT chart using a relatively smaller ASN and a shorter sampling interval (h) has a higher overall detection effectiveness.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:229:y:2013:i:2:p:411-421
    DOI: 10.1016/j.ejor.2013.03.026
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    References listed on IDEAS

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    1. Chen, Huifen & Cheng, Yuyen, 2009. "Designing charts for known autocorrelations and unknown marginal distribution," European Journal of Operational Research, Elsevier, vol. 198(2), pages 520-529, October.
    2. Morais Manuel Cabral & Pacheco António, 2006. "Combined CUSUM–Shewhart Schemes for Binomial Data," Stochastics and Quality Control, De Gruyter, vol. 21(1), pages 43-57, January.
    3. Salah Haridy & Zhang Wu & Fong-Jung Yu & Mohammad Shamsuzzaman, 2013. "An optimisation design of the combined np-CUSUM scheme for attributes," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 7(1), pages 16-37.
    4. Wang, Wenbin, 2012. "A simulation-based multivariate Bayesian control chart for real time condition-based maintenance of complex systems," European Journal of Operational Research, Elsevier, vol. 218(3), pages 726-734.
    5. Zhang Wu & Jianxin Jiao & Ying Liu, 2008. "A binomial CUSUM chart for detecting large shifts in fraction nonconforming," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(11), pages 1267-1276.
    6. 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.
    7. 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.
    8. Wu, Zhang & Luo, Hua, 2003. "Three-triplet np control charts," European Journal of Operational Research, Elsevier, vol. 149(3), pages 614-624, September.
    9. Chen, Yan-Kwang & Hsieh, Kun-Lin, 2007. "Hotelling's T2 charts with variable sample size and control limit," European Journal of Operational Research, Elsevier, vol. 182(3), pages 1251-1262, November.
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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. Shi, Wen & Kleijnen, Jack P.C. & Liu, Zhixue, 2014. "Factor screening for simulation with multiple responses: Sequential bifurcation," European Journal of Operational Research, Elsevier, vol. 237(1), pages 136-147.
    3. Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    4. Bersimis, Sotiris & Koutras, Markos V. & Maravelakis, Petros E., 2014. "A compound control chart for monitoring and controlling high quality processes," European Journal of Operational Research, Elsevier, vol. 233(3), pages 595-603.

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