IDEAS home Printed from https://ideas.repec.org/a/gam/jsusta/v15y2023i15p11797-d1207801.html
   My bibliography  Save this article

A New EWMA Control Chart for Monitoring Multinomial Proportions

Author

Listed:
  • Shengjin Gan

    (Department of Statistics, National Chengchi University, Taipei 116, Taiwan
    School of Big Data & Artificial Intelligence, Fujian Polytechnic Normal University, Fuqing 350300, China)

  • Su-Fen Yang

    (Department of Statistics, National Chengchi University, Taipei 116, Taiwan)

  • Li-Pang Chen

    (Department of Statistics, National Chengchi University, Taipei 116, Taiwan)

Abstract

Control charts have been widely used for monitoring process quality in manufacturing and have played an important role in triggering a signal in time when detecting a change in process quality. Many control charts in literature assume that the in-control distribution of the univariate or multivariate process data is continuous. This research develops two exponentially weighted moving average (EWMA) proportion control charts to monitor a process with multinomial proportions under large and small sample sizes, respectively. For a large sample size, the charting statistic depends on the well-known Pearson’s chi-square statistic, and the control limit of the EWMA proportion chart is determined by an asymptotical chi-square distribution. For a small sample size, we derive the exact mean and variance of the Pearson ’ s chi-square statistic. Hence, the exact EWMA proportion chart is determined. The proportion chart can also be applied to monitor the distribution-free continuous multivariate process as long as each categorical proportion associated with specification limits of each quality variable is known or estimated. Lastly, we examine simulation studies and real data analysis to conduct the detection performance of the proposed EWMA proportion chart.

Suggested Citation

  • Shengjin Gan & Su-Fen Yang & Li-Pang Chen, 2023. "A New EWMA Control Chart for Monitoring Multinomial Proportions," Sustainability, MDPI, vol. 15(15), pages 1-19, July.
    • Handle: RePEc:gam:jsusta:v:15:y:2023:i:15:p:11797-:d:1207801
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2071-1050/15/15/11797/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2071-1050/15/15/11797/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Su-Fen Yang & Li-Pang Chen & Cheng-Kuan Lin, 2023. "Adjustment of Measurement Error Effects on Dispersion Control Chart with Distribution-Free Quality Variable," Sustainability, MDPI, vol. 15(5), pages 1-19, February.
    2. Flávia Matias Oliveira da Silva & Karina Santos Silvério & Maria Ivone Castanheira & Mariana Raposo & Maria José Imaginário & Isabel Simões & Maria Adelaide Almeida, 2022. "Construction of Control Charts to Help in the Stability and Reliability of Results in an Accredited Water Quality Control Laboratory," Sustainability, MDPI, vol. 14(22), pages 1-11, November.
    3. Jian Li & Fugee Tsung & Changliang Zou, 2014. "Multivariate binomial/multinomial control chart," IISE Transactions, Taylor & Francis Journals, vol. 46(5), pages 526-542.
    4. Zhonghua Li & Peihua Qiu & Snigdhansu Chatterjee & Zhaojun Wang, 2013. "Using p values to design statistical process control charts," Statistical Papers, Springer, vol. 54(2), pages 523-539, May.
    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. Sotirios Bersimis & Athanasios Sachlas & Philippe Castagliola, 2017. "Controlling Bivariate Categorical Processes using Scan Rules," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1135-1149, December.
    2. Chia-Ding Hou & Rung-Hung Su, 2024. "An Outlier Detection Approach to Recognize the Sources of a Process Failure within a Multivariate Poisson Process," Mathematics, MDPI, vol. 12(18), pages 1-10, September.
    3. Ohunakin, Olayinka S. & Adaramola, Muyiwa S. & Oyewola, Olanrewaju. M. & Fagbenle, Richard O., 2014. "Solar energy applications and development in Nigeria: Drivers and barriers," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 294-301.
    4. Ricardo Saldanha Morais & Roberto da Costa Quinino & Emilio Suyama & Linda Lee Ho, 2019. "Estimators of parameters of a mixture of three multinomial distributions based on simple majority results," Statistical Papers, Springer, vol. 60(4), pages 1283-1316, August.
    5. Ali Yeganeh & Mahdi Parvizi Amineh & Alireza Shadman & Sandile Charles Shongwe & Seyed Mojtaba Mohasel, 2023. "Combination of Sequential Sampling Technique with GLR Control Charts for Monitoring Linear Profiles Based on the Random Explanatory Variables," Mathematics, MDPI, vol. 11(7), pages 1-21, March.
    6. Al-Kayiem, Hussain H. & Aja, Ogboo Chikere, 2016. "Historic and recent progress in solar chimney power plant enhancing technologies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 58(C), pages 1269-1292.
    7. Chasnyk, O. & Sołowski, G. & Shkarupa, O., 2015. "Historical, technical and economic aspects of biogas development: Case of Poland and Ukraine," Renewable and Sustainable Energy Reviews, Elsevier, vol. 52(C), pages 227-239.
    8. Joanna A. Kamińska & Guido Sciavicco & Jan K. Kazak, 2023. "Sustainable Cities and Regions—Statistical Approaches," Sustainability, MDPI, vol. 15(9), pages 1-3, May.

    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:gam:jsusta:v:15:y:2023:i:15:p:11797-:d:1207801. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.