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On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts

Author

Listed:
  • Shahid Hussain

    (Faculty of Science, Institute of Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China
    Department of Mathematics, COMSATS University Islamabad, Attock Campus, Attock 43600, Pakistan)

  • Sun Mei

    (Faculty of Science, Institute of Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China)

  • Muhammad Riaz

    (Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia)

  • Saddam Akber Abbasi

    (Department of Mathematics, Statistics, and Physics, Qatar University, Doha 2713, Qatar)

Abstract

A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption that the process is free from outliers or the estimators are correctly estimated from in-control samples. Generally, there are question marks about such kind of narratives. The performance of the mean chart is highly affected in the presence of outliers. Therefore, the median chart is an attractive alternative to the mean chart in this situation. The control charts are usually implemented in two phases: Phase I (retrospective) and Phase II (prospective/monitoring). The efficiency of any control chart in Phase II depends on the accuracy of control limits obtained from Phase I. The current study focuses on the Phase I analysis of location parameters using median control charts. We examined the performance of different auxiliary information-based median control charts and compared the results with the usual median chart. Standardized variance and relative efficacy are used as performance measures to evaluate the efficiency of median estimators. Moreover, the probability to signal measure is used to evaluate the performance of proposed control charts to detect any potential changes in the process. The results revealed that the proposed auxiliary information based median control charts perform better in Phase I analysis. In addition, a practical illustration of an industrial scenario demonstrated the significance of the proposed control charts, in which the monitoring of concrete compressive strength is emphasized.

Suggested Citation

  • Shahid Hussain & Sun Mei & Muhammad Riaz & Saddam Akber Abbasi, 2020. "On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts," Mathematics, MDPI, vol. 8(5), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:706-:d:353575
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    References listed on IDEAS

    as
    1. Faraz, Alireza & Woodall, William H. & Heuchenne, Cedric, 2015. "Guaranteed conditional performance of the S^2 control chart with estimated parameters," LIDAM Reprints ISBA 2015037, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Muhammad Riaz, 2008. "Monitoring process mean level using auxiliary information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 62(4), pages 458-481, November.
    3. Philippe Castagliola & Fernanda Otilia Figueiredo, 2013. "The median chart with estimated parameters," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 7(5), pages 594-614.
    4. Alireza Faraz & William H. Woodall & C. Heuchenne, 2015. "Guaranteed conditional performance of the S2 control chart with estimated parameters," International Journal of Production Research, Taylor & Francis Journals, vol. 53(14), pages 4405-4413, July.
    5. Faraz, Alireza & Woodall, William & Heuchenne, Cedric, 2015. "Guaranteed conditional performance of the S^2 control chart with estimated parameters," LIDAM Discussion Papers ISBA 2015004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. XueLong Hu & Philippe Castagliola & XiaoJian Zhou & AnAn Tang, 2019. "Conditional design of the EWMA median chart with estimated parameters," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(8), pages 1871-1889, April.
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