IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v228y2013i3p571-581.html
   My bibliography  Save this article

Economic and economic statistical designs of the synthetic X¯ chart using loss functions

Author

Listed:
  • Yeong, Wai Chung
  • Khoo, Michael B.C.
  • Lee, Ming Ha
  • Rahim, M.A.

Abstract

This paper proposes the economic and economic statistical designs of the synthetic X¯ chart. In the economic design, the optimal chart parameters that minimize the expected cost function are obtained, while in the economic statistical design, the optimal chart parameters are obtained by minimizing the expected cost function, subject to constraints on the in-control average run length (ARL0) and the out-of-control average run length (ARL1). A small increase in cost is incurred when the statistical constraints are added to the economic design, however, a significant improvement in statistical performance is attained. The sensitivity of the optimal cost and the chart parameters for different loss functions and input parameters is investigated. The effects of misspecification of the type of the loss function, and the Taguchi loss coefficient, as well as the risk aversion coefficient of the loss function, are also investigated. In addition, effects of the process capability index are studied. Based on numerical studies, comparisons are made between the synthetic X¯, Shewhart X¯, and EWMA charts.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:228:y:2013:i:3:p:571-581
    DOI: 10.1016/j.ejor.2013.02.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221713001549
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2013.02.021?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. Yang, S.F. & Rahim, M.A., 2005. "Economic statistical process control for multivariate quality characteristics under Weibull shock model," International Journal of Production Economics, Elsevier, vol. 98(2), pages 215-226, November.
    2. Wu, Zhang & Yang, Mei & Khoo, Michael B.C. & Yu, Fong-Jung, 2010. "Optimization designs and performance comparison of two CUSUM schemes for monitoring process shifts in mean and variance," European Journal of Operational Research, Elsevier, vol. 205(1), pages 136-150, August.
    3. Michael Khoo & V. Wong & Zhang Wu & Philippe Castagliola, 2012. "Optimal design of the synthetic chart for the process mean based on median run length," IISE Transactions, Taylor & Francis Journals, vol. 44(9), pages 765-779.
    4. Liu, Liping & Yu, Miaomiao & Ma, Yizhong & Tu, Yiliu, 2013. "Economic and economic-statistical designs of an X¯ control chart for two-unit series systems with condition-based maintenance," European Journal of Operational Research, Elsevier, vol. 226(3), pages 491-499.
    5. Kim, Michael Jong & Jiang, Rui & Makis, Viliam & Lee, Chi-Guhn, 2011. "Optimal Bayesian fault prediction scheme for a partially observable system subject to random failure," European Journal of Operational Research, Elsevier, vol. 214(2), pages 331-339, October.
    6. Lee, Pei-Hsi, 2013. "Joint statistical design of X¯ and s charts with combined double sampling and variable sampling interval," European Journal of Operational Research, Elsevier, vol. 225(2), pages 285-297.
    7. Jain, Sanjay & Triantis, Konstantinos P. & Liu, Shiyong, 2011. "Manufacturing performance measurement and target setting: A data envelopment analysis approach," European Journal of Operational Research, Elsevier, vol. 214(3), pages 616-626, November.
    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. 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.
    2. 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.
    3. Yin, Hui & Zhang, Guojun & Zhu, Haiping & Deng, Yuhao & He, Fei, 2015. "An integrated model of statistical process control and maintenance based on the delayed monitoring," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 323-333.
    4. 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.
    5. 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.
    6. 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.
    7. 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.

    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. Mukherjee, Amitava & Sen, Rudra, 2018. "Optimal design of Shewhart–Lepage type schemes and its application in monitoring service quality," European Journal of Operational Research, Elsevier, vol. 266(1), pages 147-167.
    2. 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.
    3. Yin, Hui & Zhang, Guojun & Zhu, Haiping & Deng, Yuhao & He, Fei, 2015. "An integrated model of statistical process control and maintenance based on the delayed monitoring," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 323-333.
    4. Ching-Hsin Wang & Feng-Chia Li, 2020. "Economic design under gamma shock model of the control chart for sustainable operations," Annals of Operations Research, Springer, vol. 290(1), pages 169-190, July.
    5. Jørgen Vitting Andersen & Roy Cerqueti & Giulia Rotundo, 2017. "Rational expectations and stochastic systems," Documents de travail du Centre d'Economie de la Sorbonne 17060, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Oct 2019.
    6. Peruchi, Rogério Santana & Balestrassi, Pedro Paulo & de Paiva, Anderson Paulo & Ferreira, João Roberto & de Santana Carmelossi, Michele, 2013. "A new multivariate gage R&R method for correlated characteristics," International Journal of Production Economics, Elsevier, vol. 144(1), pages 301-315.
    7. Tavana, Madjid & Ebrahimnejad, Ali & Santos-Arteaga, Francisco J. & Mansourzadeh, Seyed Mehdi & Matin, Reza Kazemi, 2018. "A hybrid DEA-MOLP model for public school assessment and closure decision in the City of Philadelphia," Socio-Economic Planning Sciences, Elsevier, vol. 61(C), pages 70-89.
    8. Robert John Kolesar & Peter Bogetoft & Vanara Chea & Guido Erreygers & Sambo Pheakdey, 2022. "Advancing universal health coverage in the COVID-19 era: an assessment of public health services technical efficiency and applied cost allocation in Cambodia," Health Economics Review, Springer, vol. 12(1), pages 1-20, December.
    9. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
    10. Kampitsis, Dimitris & Panagiotidou, Sofia, 2022. "A Bayesian condition-based maintenance and monitoring policy with variable sampling intervals," Reliability Engineering and System Safety, Elsevier, vol. 218(PA).
    11. Moura Neto, F. & Souza, P. & de Magalhães, M.S., 2019. "Determining baseline profile by diffusion maps," European Journal of Operational Research, Elsevier, vol. 279(1), pages 107-123.
    12. Piran, Fabio Antonio Sartori & Lacerda, Daniel Pacheco & Camargo, Luis Felipe Riehs & Viero, Carlos Frederico & Dresch, Aline & Cauchick-Miguel, Paulo Augusto, 2016. "Product modularization and effects on efficiency: An analysis of a bus manufacturer using data envelopment analysis (DEA)," International Journal of Production Economics, Elsevier, vol. 182(C), pages 1-13.
    13. Tan, Hua & Iqbal, Nadeem & Wu, Zhengzhong, 2022. "Evaluating the impact of stakeholder engagement for renewable energy sources and economic growth for CO2 emission," Renewable Energy, Elsevier, vol. 198(C), pages 999-1007.
    14. Pan, Xia & Jarrett, Jeffrey, 2007. "Using vector autoregressive residuals to monitor multivariate processes in the presence of serial correlation," International Journal of Production Economics, Elsevier, vol. 106(1), pages 204-216, March.
    15. Barbosa, Luziane Machado & Lacerda, Daniel Pacheco & Piran, Fabio Antonio Sartori & Dresch, Aline, 2017. "Exploratory analysis of the variables prevailing on the effects of product modularization on production volume and efficiency," International Journal of Production Economics, Elsevier, vol. 193(C), pages 677-690.
    16. 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.
    17. Ou, Yanjing & Wu, Zhang & Goh, Thong Ngee, 2011. "A new SPRT chart for monitoring process mean and variance," International Journal of Production Economics, Elsevier, vol. 132(2), pages 303-314, August.
    18. Jørgen Vitting Andersen & Roy Cerqueti & Jessica Riccioni, 2023. "Rational expectations as a tool for predicting failure of weighted k-out-of-n reliability systems," Post-Print hal-03634370, HAL.
    19. Akram Khaleghei & Viliam Makis, 2015. "Model parameter estimation and residual life prediction for a partially observable failing system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(3), pages 190-205, April.
    20. Hahn, G.J. & Brandenburg, M. & Becker, J., 2021. "Valuing supply chain performance within and across manufacturing industries: A DEA-based approach," International Journal of Production Economics, Elsevier, vol. 240(C).

    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:ejores:v:228:y:2013:i:3:p:571-581. 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/eor .

    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.