Robust adaptive exponentially weighted moving average control charts with applications of manufacturing processes

  • Hafiz Zafar NazirEmail author
  • Tahir Hussain
  • Noureen Akhtar
  • Muhammad Abid
  • Muhammad Riaz


Statistical process control (SPC) has its own importance in the field of quality control. In SPC, control charts are significant tools to monitor process parameters, and exponentially weighted moving average (EWMA) control chart is one such tool. It is a memory-type chart, which is used to target mainly the smaller shifts in the process parameters. Adaptive EWMA (AEWMA) scheme is used to identify small as well as large shifts. EWMA and AEWMA are based on the assumption of normality, which is quite hard to find in practice, and there are many situations where outliers are occasionally present. In the current study, we have proposed four robust adaptive EWMA schemes for monitoring process location parameter. We have investigated their performance under uncontaminated normal and contaminated normal environments. We have carried out comparisons amongst different competing charts based on average run length (ARL), standard deviation of run length (SDRL) and different percentiles of run length distribution. Two examples related to manufacturing processes are also provided for practical implementation of the proposed schemes.


Average run length (ARL) Robust adaptive EWMA Out-of-control (OOC) In-control (IC) Contaminated environments 



  1. 1.
    Roberts S (1959) Control chart tests based on geometric moving averages. Technometrics 1(3):239–250Google Scholar
  2. 2.
    Page E (1954) Continuous inspection schemes. Biometrika 41:100–115MathSciNetzbMATHGoogle Scholar
  3. 3.
    Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics 32(1):1–12MathSciNetGoogle Scholar
  4. 4.
    Capizzi G, Masarotto G (2003) An adaptive exponentially weighted moving average control chart. Technometrics 45(3):199–207MathSciNetGoogle Scholar
  5. 5.
    Yashchin E (1987) Some aspects of the theory of statistical control schemes. IBM J Res Dev 31(2):199–205Google Scholar
  6. 6.
    Lucas JM, Crosier RB (1982) Fast initial response for CUSUM quality-control schemes: give your CUSUM a head start. Technometrics 24(3):199–205Google Scholar
  7. 7.
    Tatum LG (1997) Robust estimation of the process standard deviation for control charts. Technometrics 39(2):127–141MathSciNetzbMATHGoogle Scholar
  8. 8.
    Moustafa A, Mokhtar BA (1999) New robust statistical process control chart for location. Qual Eng 12(2):149–159Google Scholar
  9. 9.
    Borror CM, Montgomery DC, Runger GC (2000) Robustness of the EWMA control chart to non-normality. Qual Control Appl Stat 45(2):125–128MathSciNetGoogle Scholar
  10. 10.
    Testik MC, Runger GC, Borror CM (2003) Robustness properties of multivariate EWMA control charts. Qual Reliab Eng Int 19(1):31–38Google Scholar
  11. 11.
    Abbas N, Riaz M, Does RJ (2013) Mixed exponentially weighted moving average cumulative sum charts for process monitoring. Qual Reliab Eng Int 29(3):345–356Google Scholar
  12. 12.
    De Mast J, Roes KC (2004) Robust individuals control chart for exploratory analysis. Qual Eng 16(3):407–421Google Scholar
  13. 13.
    Maravelakis PE, Panaretos J, Psarakis S (2005) An examination of the robustness to non-normality of the EWMA control charts for the dispersion. Commun Stat Simul Comput 34(4):1069–1079MathSciNetzbMATHGoogle Scholar
  14. 14.
    Abu-Shawiesh MO (2008) A simple robust control chart based on MAD. J Math Stat 4(2):102–107MathSciNetGoogle Scholar
  15. 15.
    Shahriari H, Maddahi A, Shokoui AH (2009) A robust dispersion control chart based on M-estimate. Journal of Industrial and Systems Engineering, Vol. 2. No. 4(2009):297–307Google Scholar
  16. 16.
    Nazir HZ, Riaz M, Does RJ, Abbas N (2013) Robust CUSUM control charting. Qual Eng 25(3):211–224Google Scholar
  17. 17.
    Alkahtani SS (2013) Robustness of DEWMA versus EWMA control charts to non-normal processes. J Mod Appl Stat Methods 12(1):148–163Google Scholar
  18. 18.
    Zaman B, Lee MH, Riaz M, Abujiya MAR (2017) An adaptive EWMA scheme-based CUSUM accumulation error for efficient monitoring of process location. Qual Reliab Eng Int 33(8):2463–2482Google Scholar
  19. 19.
    Abbas N (2018) Homogeneously weighted moving average control chart with an application in substrate manufacturing process. Comput Ind Eng 120:460–470Google Scholar
  20. 20.
    Haq A, Gulzar R, Khoo MB (2018) An efficient adaptive EWMA control chart for monitoring the process mean. Qual Reliab Eng Int 34(4):563–571Google Scholar
  21. 21.
    Abid M, Nazir HZ, Riaz M, Lin Z (2018) In-control robustness comparison of different control charts. Trans Inst Meas Control 40(13):3860–3871Google Scholar
  22. 22.
    Huber PJ (1981) Robust statistics. Wiley, New YorkzbMATHGoogle Scholar
  23. 23.
    Beaton AE, Tukey JW (1974) The fitting of power series, meaning polynomials, illustrated on based spectroscopic data. Technometrics 19:161–164zbMATHGoogle Scholar
  24. 24.
    Rousseeuw, PJ (1991) Tutorial to Robust Statistics. Journal of Chemometrics 5(1):1–20Google Scholar
  25. 25.
    Dixon WJ, Massey FJ (1969) Introduction to statistical analysis, 3rd edn. McGraw-Hill, New YorkzbMATHGoogle Scholar
  26. 26.
    Weisberg HF (1992). Central tendency and variability. Sage University Paper Series on Quantitative Application in Social Sciences, Series no. 07-038. A. Virding, Ed. Newbury Park: Sage.Google Scholar
  27. 27.
    Tukey JW (1977). Exploratory data analysis. Reading: Addison WesleyGoogle Scholar
  28. 28.
    Wang T, Li Y, Cui H (2007) On weighted randomly trimmed means. J Syst Sci Complex 20(1):47–65MathSciNetzbMATHGoogle Scholar
  29. 29.
    Hossain MP, Sanusi RA, Omar MH, Riaz M (2018) On designing Maxwell CUSUM control chart: an efficient way to monitor failure rates in boring processes. Int J Adv Manuf Technol 100(5–8):1923–1930 1–8Google Scholar
  30. 30.
    Mahmood T, Riaz M, Omar MH, Xie M (2018) Alternative methods for the simultaneous monitoring of simple linear profile parameters. Int J Adv Manuf Technol 97(5–8):2851–2871Google Scholar
  31. 31.
    Riaz M, Ahmad S (2016) On designing a new Tukey-EWMA control chart for process monitoring. Int J Adv Manuf Technol 82(1–4):1–23Google Scholar
  32. 32.
    Zaman B, Riaz M, Ahmad S, Abbasi SA (2015) On artificial neural networking-based process monitoring under bootstrapping using runs rules schemes. Int J Adv Manuf Technol 76(1–4):311–327Google Scholar
  33. 33.
    Ahmad S, Riaz M, Hussain S, Abbasi SA (2018) On auxiliary information-based control charts for autocorrelated processes with application in manufacturing industry. Int J Adv Manuf Technol 100(5–8):1965–1980 1–16Google Scholar
  34. 34.
    Riaz M, Mahmood T, Abbasi SA, Abbas N, Ahmad S (2017) Linear profile monitoring using EWMA structure under ranked set schemes. Int J Adv Manuf Technol 91(5–8):2751–2775Google Scholar
  35. 35.
    Zaman B, Abbas N, Riaz M, Lee MH (2016) Mixed CUSUM-EWMA chart for monitoring process dispersion. Int J Adv Manuf Technol 86(9–12):3025–3039Google Scholar
  36. 36.
    Tran K, Castagliola P, Balakrishnan N (2017) On the performance of the Shewhart median chart in presence of measurement error. Qual Reliab Eng Int 33(5):1019–1029Google Scholar
  37. 37.
    Crowder SV (1987) Average run lengths of exponentially weighted moving average control charts. J Qual Technol 19(3):161–164Google Scholar
  38. 38.
    Crowder SV (1989) Design of exponentially weighted moving average schemes. J Qual Technol 21(3):155–162Google Scholar
  39. 39.
    Haq A (2013) A new hybrid exponentially weighted moving average control chart for monitoring process mean. Qual Reliab Eng Int 29(7):1015–1025Google Scholar
  40. 40.
    Moustafa A (2009) A control chart based on robust estimators for monitoring the process mean of a quality characteristic. Int J Qual Reliab Manage 26(5):480–496Google Scholar
  41. 41.
    Schoonhoven M, Nazir HZ, Riaz M, Does RJ (2011) Robust location estimators for the X-bar control chart. J Qual Technol 43(4):363–379Google Scholar
  42. 42.
    Riaz M, Abbasi SA, Ahmad S, Zaman B (2014) On efficient phase II process monitoring charts. Int J Adv Manuf Technol 70(9–12):2263–2274Google Scholar
  43. 43.
    Montgomery DC (2009) Introduction to Statistical Quality Control, 6th ed. Wiley, New YorkGoogle Scholar

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© Springer-Verlag London Ltd., part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of ScienceUniversity of SargodhaSargodhaPakistan
  2. 2.Department of Statistics, Faculty of Science and TechnologyGovernment College UniversityFaisalabadPakistan
  3. 3.Department of Mathematics and StatisticsKing Fahad University of Petroleum and MineralsDhahranSaudi Arabia

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