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On designing a new Tukey-EWMA control chart for process monitoring

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Abstract

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts are used to detect smaller shifts in process parameters. The usual EWMA and CUSUM charts depend on the normality assumption for a better detection ability. This study proposes an efficient EWMA control chart based on the spirit of Tukey control chart, especially designed for skewed distributions. The performance of the proposed and the competing charts is measured using different length properties such as average run length (ARL), standard deviation of run length (SDRL), and median run length (MDRL). We have observed that the proposed chart is quite efficient at detecting process shifts of smaller magnitude, especially for skewed distributions. For practical considerations, the proposed chart is implemented at aerospace manufacturing data on industrial production index.

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References

  1. Ahmad S, Abbasi SA, Riaz M, Abbas N (2014) On efficient use of auxiliary information for control charting in SPC. Comput Ind Eng 67:173–184

    Article  Google Scholar 

  2. Ahmad S, Lin Z, Abbasi SA, Riaz M (2012) On efficient monitoring of process dispersion using interquartile range. Open J Appl Sci 2(4B):39–43

    Article  Google Scholar 

  3. Ahmad S, Riaz M, Abbasi SA, Lin Z (2013) On monitoring process variability under double sampling scheme. Int J Prod Econ 142(2):388–400

    Article  Google Scholar 

  4. Ahmad S, Riaz M, Abbasi SA, Lin Z (2014) On efficient median control charting. J Chin Inst Eng 37(3):358–375

    Article  Google Scholar 

  5. Alemi F (2004) Tukey’s control chart. Qual Manag Healthcare 13(4):216–221

    Article  Google Scholar 

  6. Association of Cost Engineers and the Royal Institute of Chartered Surveyors (1998) Industrial engineering projects: practice and procedures for capital projects in the engineering, manufacturing and process industries. Chapman & Hall, 2:6 Boundary Row, London SE18HN, UK

  7. Borckardt JJ, Nash MR, Hardesty S, Herbert J, Cooney H, Pelic C (2005) An empirical evaluation of Tukey’s control chart for use in health care and quality management applications. Qual Manag Healthcare 14(2):112–115

    Article  Google Scholar 

  8. Borckardt JJ, Pelic C, Herbert J, Borckardt D, Nash MR, Cooney H, Hardesty S (2006) An autocorrelation-corrected nonparametric control chart technique for health care quality applications. Qual Manag Healthcare 15(3):157–162

    Article  Google Scholar 

  9. Chakraborti S (2000) Run length, average run length, and false alarm rate of Shewhart X-bar chart: exact derivations by conditioning. Commun Stat Simul Comput 29:61–81

    Article  MATH  Google Scholar 

  10. Chen G, Cheng SW, Xie H (2004) A new EWMA control chart for monitoring both location and dispersion. Qual Technol Quant Manag 1(2):217–231

    MathSciNet  Google Scholar 

  11. Costa AFB, Rahim MA (2006) A synthetic control chart for monitoring the process mean and variance. J Qual Maint Eng 12(1):81–88

    Article  MathSciNet  Google Scholar 

  12. Crowder SV (1987) A simple method for studying run–length distributions of exponentially weighted moving average charts. Technometrics 29(4):401–407

    MathSciNet  MATH  Google Scholar 

  13. Crowder SV (1989) Design of exponentially weighted moving average schemes. J Qual Technol 21(3):155–162

    MathSciNet  Google Scholar 

  14. Frontini GF, Kennedy SL (2003) Manufacturing in real time: managers, engineers and an age of smart machines (vol. 1). Butterworth-Heinemann

  15. FWC Sector Competitiveness Studies (2009) Competitiveness of the EU aerospace industry with focus on aeronautics industry within the framework contract of sectoral competitiveness studies. ENTR/06/054, lient: European Commission, Directorate-General Enterprise & Industry

  16. Gan FF (1995) Joint monitoring of process mean and variance using exponentially weighted moving average control charts. Technometrics 37(4):446–453

    Article  MATH  Google Scholar 

  17. Hamilton MD, Crowder SV (1992) Average run lengths of EWMA control charts for monitoring a process standard deviation. J Qual Technol 24(1):44–50

    Google Scholar 

  18. Hunter JS (1986) The exponentially weighted moving average. J Qual Technol 18(4):203–210

    Google Scholar 

  19. Jones LA, Champ CW, Rigdon SE (2001) The performance of exponentially weighted moving average charts with estimated parameters. Technometrics, 43(2)

  20. Khaliq Q, Riaz M, Alemi F (2014) Performance of Tukey’s and individual/moving range control charts. Qual Reliab Eng Int. doi:10.1002/qre.1664

    Google Scholar 

  21. Lee PH (2011) The effects of Tukey’s control chart with asymmetrical control limits on monitoring of production processes. Afr J Bus Manag 5(11):4044–4050

    Google Scholar 

  22. Lee PH, Torng CC (2013) A note on “modified Tukey’s control chart”. Commun Stat Simul Comput. doi:10.1080/03610918.2013.771743, just-accepted

    Google Scholar 

  23. Lee PH, Kuo TI, Lin CS (2013) Economically optimum design of Tukey’s control chart with asymmetrical control limits for controlling process mean of skew population distribution. Eur J Ind Eng 7(6):687–703

    Article  Google Scholar 

  24. Lucas JM, Saccucci MS (1990) Exponentially weighted moving average control schemes: properties and enhancements. Technometrics 32(1):1–12

    Article  MathSciNet  Google Scholar 

  25. MacGregor JF, Harris TJ (1990) Discussion. Technometrics 32(1):23–26

    Google Scholar 

  26. Mekparyup J, Kornpetpanee S, Saithanu K (2014) The adjusted Tukey’s control chart with MADM. Int J Appl Environ Sci 9(4):2063–2075

    Google Scholar 

  27. Mekparyup J, Kornpetpanee S, Saithanu K (2014) The performance of the adjusted Tukey’s control chart under asymmetric distributions. Glob J Pure Appl Math 10(5):719–724

    Google Scholar 

  28. Montgomery DC (2009) Introduction to statistical quality control, 6th edn. Wiley, New York

    Google Scholar 

  29. Ou Y, Wu Z, Tsung F (2012) A comparison study of effectiveness and robustness of control charts for monitoring process mean. Int J Prod Econ 135(1):479–490

    Article  Google Scholar 

  30. Quesenberry CP (1993) The effects of sample size on estimated limits \( \overline{X} \) and X control charts. J Qual Technol 25:237–247

    Google Scholar 

  31. Riaz M, Abbasi SA, Ahmad S, Zaman B (2014) On efficient phase II process monitoring charts. Int J Adv Manuf Technol 70(9–12):2263–2274

    Article  Google Scholar 

  32. Riaz M, Mehmood R, Ahmad S, Abbasi SA (2013) On the performance of auxiliary-based control charting under normality and non-normality with estimation effects. Qual Reliab Eng Int 29(8):1165–1179

    Article  Google Scholar 

  33. Roberts SW (1959) Control chart tests based on geometric moving averages. Technometrics 1(3):239–250

    Article  Google Scholar 

  34. Robinson PB, Ho TY (1978) Average run lengths of geometric moving average charts by numerical methods. Technometrics 20(1):85–93

    Article  MATH  Google Scholar 

  35. Shewhart WA (1931) Economic control of quality of manufactured product. Van Nostrand, Princeton

    Google Scholar 

  36. Sukparungsee S (2012) Robustness of Tukey’s control chart in detecting a changes of parameter of skew distributions. Int J Appl Phys Math 2(5):379–382

    Article  Google Scholar 

  37. Sukparungsee S (2013) Asymmetric Tukey’s control chart robust to skew and non-skew process observation. World Acad Sci Eng Technol Int J Math Comput Sci Eng 7(8):37–40

    Google Scholar 

  38. Tercero-Gómez VG, Cordero-Franco MAE, San Nicolás de los Garza N, Alvarado-Puente R & del Carmen Temblador-Pérez M (2014) Robust estimation of variance using modified Tukey’s control chart. Proceedings of the 2014 Industrial and Systems Engineering Research Conference

  39. Tercero-Gomez V, Ramirez-Galindo J, Cordero-Franco A, Smith M, Beruvides M (2012) Modified Tukey’s control chart. Commun Stat Simul Comput 41(9):1566–1579

    Article  MathSciNet  MATH  Google Scholar 

  40. Torng CC, Lee PH (2008) ARL performance of the Tukey’s control chart. Commun Stat Simul Comput 37(9):1904–1913

    Article  MathSciNet  MATH  Google Scholar 

  41. Torng CC, Lee PH, Tseng CC (2009) An economic design of Tukey’s control chart. J Chin Inst Ind Eng 26(1):53–59

    Google Scholar 

  42. Torng CC, Liao HN, Lee PH, Wu JC (2009) Performance evaluation of a Tukey’s control chart in monitoring gamma distribution and short run processes. In Hong Kong: In Proceedings of the International Multi Conference of Engineers and Computer Scientists 2009, Hong Kong. 2009/03/18-20

  43. Yen CH, Aslam M, Jun CH (2014) A lot inspection sampling plan based on EWMA yield index. Int J Adv Manuf Technol 75(5–8):861–868

    Article  Google Scholar 

  44. Zhang L, Chen G (2002) A note on EWMA charts for monitoring mean changes in normal processes. Commun Stat Theor Methods 31(4):649–661

    Article  MATH  Google Scholar 

  45. Zhang S, Wu Z (2007) A CUSUM scheme with variable sample sizes for monitoring process shifts. Int J Adv Manuf Technol 33(9–10):977–987

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

    Qurat-Ul-Ain Khaliq

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    Muhammad Riaz

  3. Department of Mathematics, COMSATS Institute of Information Technology, Wah Cantt, 47040, Pakistan

    Shabbir Ahmad

Authors
  1. Qurat-Ul-Ain Khaliq
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  2. Muhammad Riaz
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  3. Shabbir Ahmad
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Correspondence to Qurat-Ul-Ain Khaliq.

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This manuscript is the authors’ original work and has not been published nor has it been submitted simultaneously elsewhere. Moreover, all the authors have checked the manuscript and have agreed to the submission.

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Khaliq, QUA., Riaz, M. & Ahmad, S. On designing a new Tukey-EWMA control chart for process monitoring. Int J Adv Manuf Technol 82, 1–23 (2016). https://doi.org/10.1007/s00170-015-7289-6

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  • DOI: https://doi.org/10.1007/s00170-015-7289-6

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