IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i7p3300-3309.html
   My bibliography  Save this article

Approximate distribution of demerit statistic--A bounding approach

Author

Listed:
  • Chang, Fengming M.
  • Chen, Long-Hui
  • Chen, Yueh-Li
  • Huang, Chien-Yu

Abstract

The traditional classical demerit control chart is used to plot the demerit statistic, a weighted sum of the number of defects in each category, on a control chart. The approximate normal method is usually used to obtain control limits though the distribution that depends on the values of the weights and the parameters of the Poisson distribution which may not always be normal. [Jones, L.A., Woodall, W.H., Conerly, M.D., 1999. Exact properties of demerit control charts. Journal of Quality Technology 31 (2), 207-216] used the characteristic function approach to determine the distribution of the demerit statistic. Unfortunately, the process that they used to determine the distribution needs complex integral evaluation via mathematical software packages or using the approximate truncated infinite series. Moreover, the characteristic function does not provide an accurate result easily. In this paper, a bounding approach is proposed to determine the approximate distribution of the demerit statistic. It is easy to implement and also the approximate error can be controlled to meet the desired accuracy. In addition, an example is demonstrated to illustrate the proposed method. The results indicate that the proposed approach is efficient and accurate. Finally, the performance among the approximate normal method, the characteristic function approach, and the proposed bounding approach are discussed.

Suggested Citation

  • Chang, Fengming M. & Chen, Long-Hui & Chen, Yueh-Li & Huang, Chien-Yu, 2008. "Approximate distribution of demerit statistic--A bounding approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3300-3309, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3300-3309
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(07)00431-8
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Luceno, Alberto & Puig-Pey, Jaime, 2002. "An accurate algorithm to compute the run length probability distribution, and its convolutions, for a Cusum chart to control normal mean," Computational Statistics & Data Analysis, Elsevier, vol. 38(3), pages 249-261, January.
    2. Xie, M. & He, B. & Goh, T. N., 2001. "Zero-inflated Poisson model in statistical process control," Computational Statistics & Data Analysis, Elsevier, vol. 38(2), pages 191-201, 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. Xu, Hai-Yan & Xie, Min & Goh, Thong Ngee & Fu, Xiuju, 2012. "A model for integer-valued time series with conditional overdispersion," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4229-4242.
    2. Olivier Thas & J. C. W. Rayner, 2005. "Smooth Tests for the Zero-Inflated Poisson Distribution," Biometrics, The International Biometric Society, vol. 61(3), pages 808-815, September.
    3. Helai Huang & Hong Chin, 2010. "Modeling road traffic crashes with zero-inflation and site-specific random effects," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 445-462, August.
    4. Baksh, M. Fazil & Böhning, Dankmar & Lerdsuwansri, Rattana, 2011. "An extension of an over-dispersion test for count data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 466-474, January.
    5. Knoth, Sven, 2006. "Computation of the ARL for CUSUM-S2 schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 499-512, November.
    6. Wu, Zhang & Yang, Mei & Jiang, Wei & Khoo, Michael B.C., 2008. "Optimization designs of the combined Shewhart-CUSUM control charts," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 496-506, December.
    7. Höhle, Michael & Paul, Michaela, 2008. "Count data regression charts for the monitoring of surveillance time series," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4357-4368, May.
    8. Hadi Saboori & Mahdi Doostparast, 2024. "Control Charts Based on Zero to k Inflated Power Series Regression Models and Their Applications," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 442-476, November.
    9. Baíllo, A. & Berrendero, J.R. & Cárcamo, J., 2009. "Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2628-2639, May.
    10. Jun Yang & Min Xie & Thong Ngee Goh, 2011. "Outlier identification and robust parameter estimation in a zero-inflated Poisson model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(2), pages 421-430, October.
    11. Zhale Tahmasebinejad, 2024. "Analysis of Two - Part Random Effects Model for Semi-Ordinal Longitudinal Response," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(2), pages 777-808, November.
    12. E. Bahrami Samani & Y. Amirian & M. Ganjali, 2012. "Likelihood estimation for longitudinal zero-inflated power series regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(9), pages 1965-1974, May.

    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:eee:csdana:v:52:y:2008:i:7:p:3300-3309. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.