IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v28y2001i7p875-885.html
   My bibliography  Save this article

Economic design of X charts with variable parameters: The Markov chain approach

Author

Listed:
  • Antonio Costa
  • M. A. Rahim

Abstract

This paper presents an economic design of X control charts with variable sample sizes, variable sampling intervals, and variable control limits. The sample size n, the sampling interval h, and the control limit coefficient k vary between minimum and maximum values, tightening or relaxing the control. The control is relaxed when an X value falls close to the target and is tightened when an X value falls far from the target. A cost model is constructed that involves the cost of false alarms, the cost of finding and eliminating the assignable cause, the cost associated with production in an out-of-control state, and the cost of sampling and testing. The assumption of an exponential distribution to describe the length of time the process remains in control allows the application of the Markov chain approach for developing the cost function. A comprehensive study is performed to examine the economic advantages of varying the X chart parameters.

Suggested Citation

  • Antonio Costa & M. A. Rahim, 2001. "Economic design of X charts with variable parameters: The Markov chain approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(7), pages 875-885.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:7:p:875-885
    DOI: 10.1080/02664760120074951
    as

    Download full text from publisher

    File URL: http://www.tandfonline.com/doi/abs/10.1080/02664760120074951
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664760120074951?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. Bai, D. S. & Lee, K. T., 1998. "An economic design of variable sampling interval control charts," International Journal of Production Economics, Elsevier, vol. 54(1), pages 57-64, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Abolmohammadi & A. Seif & M. H. Behzadi & M. B. Moghadam, 2021. "Economic statistical design of adaptive $$\bar{X}$$ X ¯ control charts based on quality loss functions," Operational Research, Springer, vol. 21(2), pages 1041-1080, June.
    2. Alireza Faraz & R. Kazemzadeh & Ahmad Parsian & M. Moghadam, 2012. "On the advantages of economically designed the Hotelling’s T2 control chart with variable sample sizes and sampling intervals," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(1), pages 39-53, January.
    3. Alireza Faraz & R. Kazemzadeh & M. Moghadam & Ahmad Parsian, 2012. "On the advantages of economically designed variable sample sizes and sampling intervals T 2 control chart: double warning lines scheme," Quality & Quantity: International Journal of Methodology, Springer, vol. 46(4), pages 1323-1336, June.
    4. Yan-Kwang Chen, 2009. "Economic design of T 2 control charts with the VSSI sampling scheme," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(1), pages 109-122, January.
    5. 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.

    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. 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.
    2. Liu, J.Y. & Xie, M. & Goh, T.N. & Liu, Q.H. & Yang, Z.H., 2006. "Cumulative count of conforming chart with variable sampling intervals," International Journal of Production Economics, Elsevier, vol. 101(2), pages 286-297, June.
    3. 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.
    4. Nenes, George, 2011. "A new approach for the economic design of fully adaptive control charts," International Journal of Production Economics, Elsevier, vol. 131(2), pages 631-642, June.
    5. Ho, Linda Lee & Trindade, Anderson Laécio Galindo, 2009. "Economic design of an X chart for short-run production," International Journal of Production Economics, Elsevier, vol. 120(2), pages 613-624, August.
    6. 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.
    7. 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.
    8. 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.
    9. Fong-jung Yu & Jiang-liang Hou, 2006. "Optimization of design parameters for [image omitted] control charts with multiple assignable causes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(3), pages 279-290.
    10. M. Abolmohammadi & A. Seif & M. H. Behzadi & M. B. Moghadam, 2021. "Economic statistical design of adaptive $$\bar{X}$$ X ¯ control charts based on quality loss functions," Operational Research, Springer, vol. 21(2), pages 1041-1080, June.
    11. Zhang, Cai Wen & Xie, Min & Goh, Thong Ngee, 2008. "Economic design of cumulative count of conforming charts under inspection by samples," International Journal of Production Economics, Elsevier, vol. 111(1), pages 93-104, January.
    12. Xie, M. & Tang, X. Y. & Goh, T. N., 2001. "On economic design of cumulative count of conforming chart," International Journal of Production Economics, Elsevier, vol. 72(1), pages 89-97, June.
    13. Yang, Yit-Ming & Su, Chia-Yi & Pearn, W.L., 2010. "Economic design of x¯-control charts for continuous flow process with multiple assignable causes," International Journal of Production Economics, Elsevier, vol. 128(1), pages 110-117, November.
    14. 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.
    15. Tagaras, George, 2017. "New indices for the evaluation of the statistical properties of Bayesian x¯ control charts for short runsAuthor-Name: Nikolaidis, Yiannis," European Journal of Operational Research, Elsevier, vol. 259(1), pages 280-292.
    16. Y-K Chen & H-H Chang, 2008. "Economic design of variable parameters X̄ control charts for processes with fuzzy mean shifts," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(8), pages 1128-1135, August.
    17. Chen, Yan-Kwang, 2004. "Economic design of control charts for non-normal data using variable sampling policy," International Journal of Production Economics, Elsevier, vol. 92(1), pages 61-74, November.

    More about this item

    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:taf:japsta:v:28:y:2001:i:7:p:875-885. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.