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On auxiliary information-based control charts for autocorrelated processes with application in manufacturing industry

  • Shabbir Ahmad
  • Muhammad Riaz
  • Shahid Hussain
  • Saddam Akber Abbasi
ORIGINAL ARTICLE
  • 22 Downloads

Abstract

Multivariate autoregressive (MAR) models are an attractive choice for applications in the processes related to finance, medical, and industry. For the monitoring of such processes, control chart is the most important and widely used tool of statistical process control tool kit. Moreover, the presence of auxiliary information helps in better estimation of different process parameters. The literature on use of auxiliary variables in control charts assumes independence of observations. In practice, we may come across processes dealing with autocorrelated outcomes. In such situations, a control chart usually produces high false alarms and exhibits slow detection of shifts when the process is out-of-control. This study intends to suggest some auxiliary information-based Shewhart charts for autocorrelated univariate and bivariate AR(1) processes. The proposed structures take into account the autocorrelation structure and offer more effective designs of control charts for efficient process monitoring. The performance measures used in this study are based on run length measures such as average run length, extra quadratic loss, relative average run length and performance comparison index. A detailed performance analysis is carried out to sort out the best performing charts. In addition, we have considered an application from a manufacturing process to demonstrate the implementation of the proposed charting structures in real scenario.

Keywords

Autoregressive AR(1) process Auxiliary variable Average run length ARL curves Control charts Location parameter Normal distribution 

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Notes

Acknowledgements

The author Muhammad Riaz is indebted to King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia, for providing excellent research facilities. The author Saddam Akber Abbasi would like to acknowledge the research support provided by Qatar University.

Funding information

Higher Education Commission (HEC) Pakistan provided funding for the project No. IPFP/HRD/HEC/2014/1630 under the Start-Up Research Grant Program (SRGP) (first author).

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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Shabbir Ahmad
    • 1
  • Muhammad Riaz
    • 2
  • Shahid Hussain
    • 3
  • Saddam Akber Abbasi
    • 4
  1. 1.Department of MathematicsCOMSATS University Islamabad, Wah CampusWah CanttPakistan
  2. 2.Department of Mathematics and StatisticsKing Fahad University of Petroleum and MineralsDhahranSaudi Arabia
  3. 3.Department of MathematicsCOMSATS University Islamabad, Attock CampusAttockPakistan
  4. 4.Department of Mathematics, Statistics and PhysicsQatar UniversityDohaQatar

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