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Optimized np Attribute Control Chart Using Triple Sampling

Author

Listed:
  • Jose Jorge Muñoz

    (Facultad de Ingeniería, Universidad del Magdalena, Santa Marta 470004, Colombia)

  • Manuel J. Campuzano

    (Facultad de Ingeniería, Universidad del Magdalena, Santa Marta 470004, Colombia)

  • Jaime Mosquera

    (Escuela de Estadística, Universidad del Valle, Cali 760032, Colombia)

Abstract

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length ( ARL ) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length ( A R L 1 ). Tables of A R L 1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of A R L 1 detecting small and moderate shifts in the process nonconforming rate in-control ( p 0 ) compared with MDSRS and DS-np.

Suggested Citation

  • Jose Jorge Muñoz & Manuel J. Campuzano & Jaime Mosquera, 2022. "Optimized np Attribute Control Chart Using Triple Sampling," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3791-:d:942471
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    References listed on IDEAS

    as
    1. 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.
    2. Muhammad Aslam & Muhammad Azam & Nasrullah Khan & Chi-Hyuck Jun, 2015. "A mixed control chart to monitor the process," International Journal of Production Research, Taylor & Francis Journals, vol. 53(15), pages 4684-4693, August.
    3. Seyed Niaki & Mohammad Ershadi, 2012. "A parameter-tuned genetic algorithm for statistically constrained economic design of multivariate CUSUM control charts: a Taguchi loss approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(12), pages 2275-2287.
    4. Wenhui Zhou & Qiang Wan & Yanfang Zheng & Yong-wu Zhou, 2017. "A joint-adaptive np control chart with multiple dependent state sampling scheme," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 6967-6979, July.
    5. 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.
    6. Faijun Nahar Mim & Michael B. C. Khoo & Sajal Saha & Philippe Castagliola, 2022. "Revised triple sampling control charts for the mean with known and estimated process parameters," International Journal of Production Research, Taylor & Francis Journals, vol. 60(16), pages 4911-4935, August.
    Full references (including those not matched with items on IDEAS)

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