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Arabian Journal for Science and Engineering

, Volume 44, Issue 3, pp 2467–2485 | Cite as

New Interquartile Range EWMA Control Charts with Applications in Continuous Stirred Tank Rector Process

  • Shahid HussainEmail author
  • Lixin SongEmail author
  • Shabbir Ahmad
  • Muhammad Riaz
Research Article - Systems Engineering
  • 45 Downloads

Abstract

Monitoring of process parameters via control charts is exceptionally common exercise in statistical process control (SPC). The exponentially weighted moving average (EWMA) control chart is one of an outstanding powerful tool of the SPC for monitoring of process parameters. The performance of any process can be improved by the careful monitoring and removing of assignable causes of variation. The existence of outliers may influence the performance of traditional charts in the monitoring of a process. This study is planned for the monitoring of dispersion parameter through the interquartile range (IQR). We proposed EWMA-type IQR charts based on auxiliary information for the efficient monitoring of process dispersion for the process following bivariate normal distribution. The comparison of these charts is made with usual IQR chart as well as traditional R and S charts. We evaluate the efficiency of charts by some commonly used run length measures. Both contaminated and uncontaminated processes are considered in this study to examine the robustness of charts. The results revealed that our proposed control charts exhibit superior performance in the presence of outliers. A real application of our study is also provided based on non-iso-thermal continuous stirred tank chemical reactor process.

Keywords

EWMA control charts Average run length (ARL) Auxiliary information Interquartile range EQL RARL PCI 

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References

  1. 1.
    Shewhart, W.A.: Some applications of statistical methods to the analysis of physical and engineering data. Bell Labs Tech. J. 3(1), 43–87 (1924)CrossRefGoogle Scholar
  2. 2.
    Montgomery, D.C.: Introduction to Statistical Quality Control. Wiley, New York (2007)zbMATHGoogle Scholar
  3. 3.
    Page, E.: Continuous inspection schemes. Biometrika 41(1/2), 100–115 (1954)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Roberts, S.: Control chart tests based on geometric moving averages. Technometrics 1(3), 239–250 (1959)CrossRefGoogle Scholar
  5. 5.
    Hawkins, D.; Olwell, D.: Cumulative Sum Charts and Charting for Quality Improvement. Springer, New York (1998)CrossRefzbMATHGoogle Scholar
  6. 6.
    Huang, W.; Shu, L.; Woodall, W.H.; Tsui, K.-L.: CUSUM procedures with probability control limits for monitoring processes with variable sample sizes. IIE Trans. 48(8), 759–771 (2016).  https://doi.org/10.1080/0740817x.2016.1146422 CrossRefGoogle Scholar
  7. 7.
    Nazir, H.Z.; Riaz, M.; Does, R.J.: Robust CUSUM control charting for process dispersion. Qual. Reliab. Eng. Int. 31(3), 369–379 (2015)CrossRefGoogle Scholar
  8. 8.
    Nazir, H.Z.; Riaz, M.; Does, R.J.; Abbas, N.: Robust CUSUM control charting. Qual. Eng. 25(3), 211–224 (2013)CrossRefGoogle Scholar
  9. 9.
    Sanusi, R.A.; Abbas, N.; Riaz, M.: On efficient CUSUM-type location control charts using auxiliary information. Qual. Technol. Quant. Manag. 15(1), 87–105 (2018)CrossRefGoogle Scholar
  10. 10.
    Yang, L., Pai, S., Wang, Y.-R.: A novel CUSUM median control chart. In: Ao, S.I., Castillo, O., Douglas, C., Feng, D.D., Lee, J.A. (eds.) International Multiconference of Engineers and Computer Scientists. Lecture Notes in Engineering and Computer Science, pp. 1707-+. (2010)Google Scholar
  11. 11.
    Abbas, N.; Riaz, M.; Does, R.J.: Enhancing the performance of EWMA charts. Qual. Reliab. Eng. Int. 27(6), 821–833 (2011)CrossRefGoogle Scholar
  12. 12.
    Abbasi, S.A.; Riaz, M.; Miller, A.; Ahmad, S.; Nazir, H.Z.: EWMA dispersion control charts for normal and non-normal processes. Qual. Reliab. Eng. Int. 31(8), 1691–1704 (2015)CrossRefGoogle Scholar
  13. 13.
    Abujiya, M.R.; Lee, M.H.; Riaz, M.: New EWMA S-2 control charts for monitoring of process dispersion. Scientia Iranica 24(1), 378–389 (2017)CrossRefGoogle Scholar
  14. 14.
    Abujiya, M.R.; Riaz, M.; Lee, M.H.: Enhancing the performance of combined Shewhart-EWMA charts. Qual. Reliab. Eng. Int. 29(8), 1093–1106 (2013).  https://doi.org/10.1002/qre.1461 CrossRefGoogle Scholar
  15. 15.
    Crowder, S.V.; Hamilton, M.D.: An EWMA for monitoring a process standard deviation. J. Qual. Technol. 24(1), 12–21 (1992b)CrossRefGoogle Scholar
  16. 16.
    Shu, L.; Jiang, W.: A new EWMA chart for monitoring process dispersion. J. Qual. Technol. 40(3), 319–331 (2008)CrossRefGoogle Scholar
  17. 17.
    Haq, A.; Brown, J.; Moltchanova, E.; Al-Omari, A.I.: Improved exponentially weighted moving average control charts for monitoring process mean and dispersion. Qual. Reliab. Eng. Int. 31(2), 217–237 (2015)CrossRefGoogle Scholar
  18. 18.
    Azam, M.; Arshad, A.; Aslam, M.; Jun, C.-H.: A control chart for monitoring the process mean using successive sampling over two occasions. Arab. J. Sci. Eng. 42(7), 2915–2926 (2017).  https://doi.org/10.1007/s13369-016-2376-z CrossRefGoogle Scholar
  19. 19.
    Ahmad, S.; Riaz, M.; Abbasi, S.A.; Lin, Z.: On efficient median control charting. J. Chin. Inst. Eng. 37(3), 358–375 (2014)CrossRefGoogle Scholar
  20. 20.
    Ahmad, S.; Abbasi, S.A.; Riaz, M.; Abbas, N.: On efficient use of auxiliary information for control charting in SPC. Comput. Ind. Eng. 67, 173–184 (2014)CrossRefGoogle Scholar
  21. 21.
    Riaz, M.; Mehmood, R.; Ahmad, S.; Abbasi, S.A.: On the performance of auxiliary-based control charting under normality and nonnormality with estimation effects. Qual. Reliab. Eng. Int. 29(8), 1165–1179 (2013)CrossRefGoogle Scholar
  22. 22.
    Ahmad, S.; Lin, Z.; Abbasi, S.A.; Riaz, M.: On efficient monitoring of process dispersion using interquartile range. Open J. Appl. Sci. 2(04), 39 (2013)CrossRefGoogle Scholar
  23. 23.
    Abbas, N.; Riaz, M.; Does, R.J.: An EWMA-type control chart for monitoring the process mean using auxiliary information. Commun. Stat. Theory Methods 43(16), 3485–3498 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Sanusi, R.A.; Riaz, M.; Abbas, N.: Combined Shewhart CUSUM charts using auxiliary variable. Comput. Ind. Eng. 105, 329–337 (2017)CrossRefGoogle Scholar
  25. 25.
    Tailor, R.; Chouhan, S.; Tailor, R.; Garg, N.: A ratio-cum-product estimator of population mean in stratified random sampling using two auxiliary variables. Statistica 72(3), 287–297 (2012)zbMATHGoogle Scholar
  26. 26.
    Lee, H.; Aslam, M.; Shakeel, Q.U.A.; Lee, W.; Jun, C.-H.: A control chart using an auxiliary variable and repetitive sampling for monitoring process mean. J. Stat. Comput. Simul. 85(16), 3289–3296 (2015)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Shabbir, J.; Gupta, S.; Hussain, Z.: Improved estimation of finite population median under two-phase sampling when using two auxiliary variables. Scientia Iranica 22(3), 1271–1277 (2015)Google Scholar
  28. 28.
    Shewhart, W.A.: Economic control of quality of manufactured product. D. Van Nostrand", (reprinted by the American Society for Quality Control in: Milwauker, p. 1931. ASQ Quality Press, WI) (1980)Google Scholar
  29. 29.
    Riaz, M.: A dispersion control chart. Commun. Stat. Simul. Comput.® 37(6), 1239–1261 (2008a)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Abbasi, S.A.; Miller, A.: On proper choice of variability control chart for normal and non-normal processes. Qual. Reliab. Eng. Int. 28(3), 279–296 (2012)CrossRefGoogle Scholar
  31. 31.
    Rocke, D.M.: Robust control charts. Technometrics 31(2), 173–184 (1989)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Tatum, L.G.: Robust estimation of the process standard deviation for control charts. Technometrics 39(2), 127–141 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Rocke, D.M.: X_Q and R_Q Charts: Robust control charts. Stat., 97–104 (1992)Google Scholar
  34. 34.
    David, H.: Early sample measures of variability. Stat. Sci. 13(4), 368–377 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Ahmad, S.; Riaz, M.: Process monitoring using quantiles control charts. J. Test. Eval. 42(4), 962–979 (2014)Google Scholar
  36. 36.
    Abbasi, S.A.; Miller, A.: MDEWMA chart: an efficient and robust alternative to monitor process dispersion. J. Stat. Comput. Simul. 83(2), 247–268 (2013)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Riaz, M.: On enhanced interquartile range charting for process dispersion. Qual. Reliab. Eng. Int. 31(3), 389–398 (2015)CrossRefGoogle Scholar
  38. 38.
    Silverman, B.W.: Density Estimation for Statistics and Data Analysis. CRC Press, Boca Raton (1986)CrossRefzbMATHGoogle Scholar
  39. 39.
    Martínez-Miranda, M.; Rueda, M.; Arcos, A.: Looking for optimal auxiliary variables in sample survey quantile estimation. Statistics 41(3), 241–252 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Ahmad, S.; Riaz, M.; Abbasi, S.A.; Lin, Z.: On median control charting under double sampling scheme. Euro. J. Ind. Eng. 8(4), 478–512 (2014)CrossRefGoogle Scholar
  41. 41.
    Ahmad, S.; Riaz, M.; Abbasi, S.A.; Lin, Z.: On monitoring process variability under double sampling scheme. Int. J. Prod. Econ. 142(2), 388–400 (2013)CrossRefGoogle Scholar
  42. 42.
    Sukhatme, P.V.; Sukhatme, P.V.: Sampling theory of surveys with applications. In. Asia Publishing House, New edition edition (1970)Google Scholar
  43. 43.
    del Mar Rueda, M.; Arcos, A.; Martínez, M.D.: Difference estimators of quantiles in finite populations. Test 12(2), 481–496 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Khaliq, Q.-U.-A.; Riaz, M.; Ahmad, S.: On designing a new Tukey-EWMA control chart for process monitoring. Int. J. Adv. Manuf. Technol. 82(1–4), 1–23 (2016)CrossRefGoogle Scholar
  45. 45.
    Riaz, M.: Control charting and survey sampling techniques in process monitoring. J. Chin. Instit. Eng. 38(3), 342–354 (2015)CrossRefGoogle Scholar
  46. 46.
    Zaman, B.; Riaz, M.; Abbas, N.; Does, R.J.: Mixed cumulative sum-exponentially weighted moving average control charts: an efficient way of monitoring process location. Qual. Reliab. Eng. Int. 31(8), 1407–1421 (2015)CrossRefGoogle Scholar
  47. 47.
    Schaffer, J.R.; Kim, M.-J.: Number of replications required in control chart Monte Carlo simulation studies. Commun. Stat. Simul. Comput.® 36(5), 1075–1087 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  48. 48.
    Marlin, T.E.: Process Control: Designing Processes and Control Systems for Dynamic Performance, 2nd edn. McGraw-Hill Higher Education, Singapore (2000)Google Scholar
  49. 49.
    Yoon, S.Y.; MacGregor, J.F.: Fault diagnosis with multivariate statistical models part I: using steady state fault signatures. J. Process Control 11(4), 387–400 (2001).  https://doi.org/10.1016/s0959-1524(00)00008-1 CrossRefGoogle Scholar
  50. 50.
    Xiangrong, S.; Yan, L.; ZhengShun, F.; Jun, L.: A multivariable statistical process monitoring method based on multiscale analysis and principal curves. Int. J. Innov. Comput. Inf. Control 9(4), 1781–1800 (2013)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.School of Mathematical SciencesDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Department of MathematicsCOMSATS Institute of Information TechnologyAttockPakistan
  3. 3.Department of MathematicsCOMSATS Institute of Information TechnologyWah CanttPakistan
  4. 4.Department of Mathematics and StatisticsKing Fahad University of Petroleum and MineralsDhahranSaudi Arabia

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