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A comparison study of three non-parametric control charts to detect shift in location parameters

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Abstract

Control charts are used as a statistical process control or SPC tool to identify the presence of assignable cause of variation in the process. Despite immense use and acceptability of parametric control charts, non-parametric control charts are an emerging area of recent development in the theory of SPC. The main advantage of non-parametric control charts is that they do not require any knowledge about the underlying distribution of the variable. In this work, we have summarized the different non-parametric control charts for controlling location from a literature survey, viz. control charts based on the sign test, control charts based on the Hodges–Lehmann estimator and control charts based on the Mann–Whitney statistic and compared their efficiency to detect the shift in location while in out of the control state under different situations and identified the best method under the prevailing situation.

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References

  1. Alloway JA, Raghavachari M (1991) Control chart based on Hodges–Lehmann estimator. J Qual Technol 23:336–347

    Google Scholar 

  2. Ferrell EB (1953) Control charts using Midranges and Medians. Ind Qual Control 9:30–34

    Google Scholar 

  3. Jacobs DC (1990) Statistical process control: watch for nonnormal distributions. Chem Eng Prog 86:19–27

    Google Scholar 

  4. Langenberg P, Iglewicz B (1986) Trimmed mean \(\overline X \) and R charts. J Qual Technol 18:152–161

    Google Scholar 

  5. Shewhart WA (1986) Statistical methods from the viewpoint of quality control. Republished in 1986 by Dover, New York

    Google Scholar 

  6. Tukey JW (1960) A survey of sampling from contaminated distributions. In: Olkin I et al (ed) Contributions of probability and statistics, essay in honor of harold hotelling. Stanford University Press, Palo Alto

    Google Scholar 

  7. Woodall WH (2000) Controversies and contradictions in statistical process control. J Qual Technol 32:341–378

    Google Scholar 

  8. Woodall WH, Montgomery DC (1999) Research issues and ideas in statistical process control. J Qual Technol 31:376–386

    Google Scholar 

  9. Yourstone SA, Zimmer WJ (1992) Non-normality and the design of control charts for averages. Decis Sci 23:1099–1113 DOI 10.1111/j.1540–5915.1992.tb00437.x

    Article  Google Scholar 

  10. Gunter BH (1989) The use and abuse of Cpk, part-2. Qual Prog 22:108–109

    Google Scholar 

  11. Lehmann EL (1963) Non-parametric confidence intervals for shift parameter. The Ann Math Stat 34:1507–1512 DOI 10.1214/aoms/1177703882

    Article  MATH  MathSciNet  Google Scholar 

  12. Noble CE (1951) Variations in conventional control charts. Ind Qual Control 8:17–22

    Google Scholar 

  13. Bradley JV (1971) A large-scale sampling study of the central limit effect. J Qual Technol 3:51–68

    Google Scholar 

  14. Bradley JV (1973) The central limit effect for a variety of population moments. J Qual Technol 5:171–177

    Google Scholar 

  15. Burr IW (1967) The effect of non-normality on constants for \(\overline X \) and R charts. Ind Qual Control 23:563–568

    Google Scholar 

  16. Schilling EG (1976) The effect of non-normality on the control limits of charts. J Qual Technol 8:183–188

    Google Scholar 

  17. Hiller FS (1969) \(\overline X \) and chart control limits based on a small number of subgroups. J Qual Technol 1:17–26

    Google Scholar 

  18. Yang C, Hiller FS (1970) Mean and variance control chart limits based on a small number of subgroups. J Qual Technol 2:9–16

    Google Scholar 

  19. Chakraborti S, Van der Lann P, Van de Wiel MA (2001) Nonparametric control charts: an overview and some results. J Qual Technol 33:304–315

    Google Scholar 

  20. Bakir ST (2001) Classification of distribution free control charts. Proceedings of annual meeting of American Statistical Association, Aug 5–9,2001, Section Quality and Productivity

  21. Albers W, Kallenberg WCM, Nurdiati S (2003) Normal, parametric and nonparametric control charts, a data driven choice. Memorandum No 1674, University of Twente, Netherlands, ISSN 0169–2690

  22. Hackl P, Ledolter J (1991) A control chart based on ranks. J Qual Technol 23(2):117–126

    Google Scholar 

  23. Pyzdek T (1995) Why normal distributions aren’t [all that normal]. Qual Eng 7(4):769–777 DOI 10.1080/08982119508918823

    Article  Google Scholar 

  24. Amin RW, Reynolds MR Jr, Bakir ST (1995) Nonparametric quality control charts based on the sign statistic. Commun Stat, Theory Methods 24:1579–1623 DOI 10.1080/03610929508831574

    MathSciNet  Google Scholar 

  25. Arnold B (1985) The sign test in current control. Statistische Hefte 26:253–262

    Article  MATH  MathSciNet  Google Scholar 

  26. Arnold B (1986) Comparison of approximate and exact optimum economic design of control charts based on the sign test. Statistische Hefte 27:239–241

    Article  MathSciNet  Google Scholar 

  27. Bakir ST, Reynolds MR (1979) A nonparametric procedure for process control based on within group ranking. Technometrics 21:175–183 DOI 10.2307/1268514

    Article  MATH  Google Scholar 

  28. Altukife FS (2003) A new nonparametric control charts based on the observations exceeding the grand median. Pak J Stat 19(3):343–351

    MATH  MathSciNet  Google Scholar 

  29. Park C, Reynolds MR Jr (1987) Nonparametric procedures for monitoring a location parameter based on linear placement statistics. Seq Anal 6:303–323 DOI 10.1080/07474948708836134

    Article  MATH  MathSciNet  Google Scholar 

  30. Orban J, Wolfe DA (1982) A class of distribution-free two-sample tests based on placements. J Am Stat Assoc 77:666–672 DOI 10.2307/2287734

    Article  MATH  MathSciNet  Google Scholar 

  31. Pappanastos EA, Adams BM (1996) Alternative designs of the Hodges–Lehmann control chart. J Qual Technol 28:213–223

    Google Scholar 

  32. Chakraborti S, Van de Wiel MA (2004) A nonparametric control chart based on the mann-whitney statistic. SPOR report, 2003, September, No:24, Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands

  33. Bakir ST (2006) Distribution-free quality control charts based on signed rank like statistics. Commun Stat, Theory Methods 35:743–757 DOI 10.1080/03610920500498907

    Article  MATH  MathSciNet  Google Scholar 

  34. Chakraborti S, Eryilmaz S (2007) A non-parametric shewhart type signed rank control chart based on runs. Commun Stat, Simul Comput 36:335–356 DOI 10.1080/03610910601158427

    Article  MATH  MathSciNet  Google Scholar 

  35. Qiu P, Hawkins DM (2003) A nonparametric multivariate CUSUM procedure for detecting shifts in all directions. Statistician 52:151–164 DOI 10.1111/1467-9884.00348

    MathSciNet  Google Scholar 

  36. Bhattacharya PK, Frierson DA (1981) A non-parametric control chart for detecting small disorders. Ann Stat 9:544–554 DOI 10.1214/aos/1176345458

    Article  MATH  MathSciNet  Google Scholar 

  37. Pettitt AN (1979) A non-parametric approach to the change-point problem. Appl Stat 28:126–135 DOI 10.2307/2346729

    Article  MATH  MathSciNet  Google Scholar 

  38. Niaki and Abbasi (2005) Fault diagnosis in multivariate control charts using artificial neural networks. Qual Reliab Eng Int l-21(8):825–840

    Article  Google Scholar 

  39. Das N, Prakash V (2007) Interpreting the out of control signal in multivariate control chart – A comparative study. Int J Adv Manuf Technol, DOI 10.1007/s00170-007-1030-z

  40. Zhou et al (2007) http://mirror.math.nankai.edu.cn/nankaisource/pre/preprint06/06-16.pdf

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Das, N. A comparison study of three non-parametric control charts to detect shift in location parameters. Int J Adv Manuf Technol 41, 799–807 (2009). https://doi.org/10.1007/s00170-008-1524-3

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