IDEAS home Printed from https://ideas.repec.org/a/bpj/ecqcon/v21y2006i2p251-260n8.html
   My bibliography  Save this article

Probability Weighted Moments Approach to Quality Control Charts

Author

Listed:
  • Muhammad Faqir

    (Department of Mathematics and Statistics, Allama Iqbal Open University, Islamabad, Pakistan)

  • Riaz Muhammad

    (Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan)

Abstract

A new control chart namely Spw-Chart for monitoring the changes in the process variability is proposed and is based on Probability Weighted Moments (PWMs) and assuming that the quality characteristic follows a normal distribution. The coefficients r2 and r3 (similar as the d2 and d3 coefficients used for R-Charts) are derived for sample sizes n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by means of a simulation study. The quantiles of which are used for determining the values of the control limits and the power of the Spw-Chart to detect shifts in process variability, are also derived for n = 2, 3, . . . , 20, 25, 30, 35, 50, 100 by simulation. Each of the simulation studies is based on 10,000 random samples from the corresponding normal distribution. The performance of Spw-Chart is investigated by comparing its power curves with those of R and S Charts. It is observed that the power curves of the Spw-Chart are above those of the R-Chart, while slightly below those of the S-Chart in detecting shifts in the process variability. The effect of non-normality on the designs of S, R, and Spw Charts, is studied by simulating random samples from the exponential and the t distributions. The simulations reveal superiority of the Spw-Chart over both R and S Charts in the sense that the power curve of Spw-Chart is least affected by non-normality among all the three charts under study.

Suggested Citation

  • Muhammad Faqir & Riaz Muhammad, 2006. "Probability Weighted Moments Approach to Quality Control Charts," Stochastics and Quality Control, De Gruyter, vol. 21(2), pages 251-260, January.
    • Handle: RePEc:bpj:ecqcon:v:21:y:2006:i:2:p:251-260:n:8
    DOI: 10.1515/EQC.2006.251
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/EQC.2006.251
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/EQC.2006.251?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. E. Collani, 1999. "Control of production processes subjectto random shocks," Annals of Operations Research, Springer, vol. 91(0), pages 289-304, 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. Muhammad Riaz & Ronald Does, 2009. "A process variability control chart," Computational Statistics, Springer, vol. 24(2), pages 345-368, May.

    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. von Collani Elart & Baur Karl, 2002. "Prediction Intervals, Tolerance Intervals and Standards in Quality Control - Part 1," Stochastics and Quality Control, De Gruyter, vol. 17(1), pages 81-98, January.
    2. Thaga K. & Kgosi P. M. & Gabaitiri L., 2007. "Max-Chart for Autocorrelated Processes," Stochastics and Quality Control, De Gruyter, vol. 22(1), pages 87-105, January.
    3. Reza Ahmadi, 2014. "Optimal maintenance scheduling for a complex manufacturing system subject to deterioration," Annals of Operations Research, Springer, vol. 217(1), pages 1-29, June.
    4. Turnes Osiris & Lee Ho Linda & Imaña Christian Rainier, 2002. "Comparison of Semi-Economic and -R Control Charts for Non-Ageing and Ageing Process," Stochastics and Quality Control, De Gruyter, vol. 17(1), pages 99-112, January.

    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:bpj:ecqcon:v:21:y:2006:i:2:p:251-260:n:8. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.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.