IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v84y2022i1d10.1007_s13571-021-00249-y.html
   My bibliography  Save this article

Economic Statistical Design for Three-level Control Charts with Variable Sample Size

Author

Listed:
  • Reza Pourtaheri

    (Allameh Tabataba’i University)

Abstract

The problem of Statistical Process Control with some discrete level classification scheme, have been recently discussed by some authors. This paper presents economic and economic-statistical designs for variable sample size (VSS) of the three-level control charts. The expected cost per unit of time is derived with the use of the cost model developed for the control chart proposed by Costa and Rahim. The genetic algorithm is employed to search for the optimal values of model parameters. Finally, the expected cost per unit of time of VSS and fixed ratio sampling (FRS) three-level control charts is compared.

Suggested Citation

  • Reza Pourtaheri, 2022. "Economic Statistical Design for Three-level Control Charts with Variable Sample Size," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 130-145, May.
    • Handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00249-y
    DOI: 10.1007/s13571-021-00249-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-021-00249-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13571-021-00249-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tzong-Ru Tsai & Wen-Pin Yen, 2011. "Exponentially weighted moving average control charts for three-level products," Statistical Papers, Springer, vol. 52(2), pages 419-429, May.
    2. Chenglong Li & Amitava Mukherjee & Qin Su & Min Xie, 2016. "Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7259-7273, December.
    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. S. H. Patil & D. T. Shirke, 2017. "Economic design of non parametric sign control chart," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(18), pages 8987-8998, September.
    5. F L Chen & C H Yeh, 2011. "Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 750-759, April.
    6. Alireza Faraz & M. Moghadam, 2009. "Hotelling’s T 2 control chart with two adaptive sample sizes," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(6), pages 903-912, November.
    7. Prabhu, Sharad S. & Montgomery, Douglas C. & Runger, George C., 1997. "Economic-statistical design of an adaptive chart," International Journal of Production Economics, Elsevier, vol. 49(1), pages 1-15, March.
    8. Chao-Yu Chou & Chung-Ho Chen & Hui-Rong Liu, 2006. "Economic Design of EWMA Charts with Variable Sampling Intervals," Quality & Quantity: International Journal of Methodology, Springer, vol. 40(6), pages 879-896, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)," Papers 1708.06160, arXiv.org.
    2. 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.
    3. 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.
    4. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    5. De Magalhaes, Maysa S. & Moura Neto, Francisco D., 2005. "Joint economic model for totally adaptive and R charts," European Journal of Operational Research, Elsevier, vol. 161(1), pages 148-161, February.
    6. De Magalhaes, Maysa S. & B. Costa, Antonio F. & Moura Neto, Francisco D., 2006. "Adaptive control charts: A Markovian approach for processes subject to independent disturbances," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 236-246, February.
    7. Linderman, Kevin & McKone-Sweet, Kathleen E. & Anderson, John C., 2005. "An integrated systems approach to process control and maintenance," European Journal of Operational Research, Elsevier, vol. 164(2), pages 324-340, July.
    8. Lei Yong Lee & Michael Boon Chong Khoo & Sin Yin Teh & Ming Ha Lee, 2015. "A Variable Sampling Interval Synthetic Xbar Chart for the Process Mean," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-18, May.
    9. Asghar Seif & Alireza Faraz & C�dric Heuchenne & Erwin Saniga & M. B. Moghadam, 2011. "A modified economic-statistical design of the T-super-2 control chart with variable sample sizes and control limits," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2459-2469, January.
    10. Chen, Yan-Kwang, 2007. "Adaptive sampling enhancement for Hotelling's T2 charts," European Journal of Operational Research, Elsevier, vol. 178(3), pages 841-857, May.
    11. Mahadik Shashibhushan B. & Shirke Digambar T., 2007. "Economic Design of A Modified Variable Sample Size and Sampling Interval Chart," Stochastics and Quality Control, De Gruyter, vol. 22(2), pages 273-293, January.
    12. CHEN, Piao & YE, Zhi-Sheng, 2018. "A systematic look at the gamma process capability indices," European Journal of Operational Research, Elsevier, vol. 265(2), pages 589-597.
    13. Celano, Giovanni & De Magalhães, Maysa S. & Costa, Antonio F.B. & Fichera, Sergio, 2011. "A stochastic shift model for economically designed charts constrained by the process stage configuration," International Journal of Production Economics, Elsevier, vol. 132(2), pages 315-325, August.
    14. Chen, Yan-Kwang & Hsieh, Kun-Lin & Chang, Cheng-Chang, 2007. "Economic design of the VSSI control charts for correlated data," International Journal of Production Economics, Elsevier, vol. 107(2), pages 528-539, June.
    15. João Nicolau & Flavio Riedlinger, 2015. "Estimation and inference in multivariate Markov chains," Statistical Papers, Springer, vol. 56(4), pages 1163-1173, November.
    16. M. A. Pasha & M. Bameni Moghadam & M. A. Rahim, 2020. "Effects of non-normal quality data on the integrated model of imperfect maintenance, early replacement, and economic design of $${\bar{X}}$$ X ¯ -control charts," Operational Research, Springer, vol. 20(4), pages 2519-2536, December.
    17. Lin, Yu-Chang & Chou, Chao-Yu, 2005. "On the design of variable sample size and sampling intervals charts under non-normality," International Journal of Production Economics, Elsevier, vol. 96(2), pages 249-261, May.
    18. Ali Salmasnia & Mohammadreza Namdar & Mina Abolfathi & Parinaz Ajaly, 2021. "Statistical design of a VSI-EWMA control chart for monitoring the communications among individuals in a weighted social network," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(3), pages 495-508, June.
    19. 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.
    20. Kim Phuc Tran & Philippe Castagliola & Giovanni Celano, 2018. "Monitoring the ratio of population means of a bivariate normal distribution using CUSUM type control charts," Statistical Papers, Springer, vol. 59(1), pages 387-413, March.

    More about this item

    Keywords

    Primary 62P30; Secondary 60J20.;

    JEL classification:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankhb:v:84:y:2022:i:1:d:10.1007_s13571-021-00249-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.