Monitoring the coefficient of variation using a variable sample size control chart

  • Philippe Castagliola
  • Ali Achouri
  • Hassen Taleb
  • Giovanni Celano
  • Stelios Psarakis
ORIGINAL ARTICLE

Abstract

This paper proposes an adaptive Shewhart control chart implementing a variable sample size strategy in order to monitor the coefficient of variation. The goals of this paper are as follows: (a) to propose an easy-to-use 3-parameter logarithmic transformation for the coefficient of variation in order to handle the variable sample size aspect; (b) to derive the formulas for computing the average run length, the standard deviation run length, and the average sample size and to evaluate the performance of the proposed chart based on these criteria; (c) to present ready-to-use tables with optimal chart parameters minimizing the out-of-control average run length as well as the out-of-control average sample size; and (d) to compare this chart with the fixed sampling rate, variable sampling interval, and synthetic control charts. An example illustrates the use of the variable sample size control chart on real data gathered from a casting process.

Keywords

Coefficient of variation Variable sample size Lognormal transformation Average run length Average sample size Casting process 

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References

  1. 1.
    Annadi H, Keats J, Runger G, Montgomery D (1995) An adaptive sample size CUSUM control chart. Int J Prod Res 33:1605–1616MATHCrossRefGoogle Scholar
  2. 2.
    Calzada M, Scariano S (2013) A synthetic control Chart for the coefficient of variation. J Stat Comput Simul 83(5):853–867MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Castagliola P (2005) A new S 2-EWMA control chart for monitoring the process variance. Qual Reliab Eng Int 21(8):781–794CrossRefGoogle Scholar
  4. 4.
    Castagliola P, Celano G, Psarakis S (2011) Monitoring the coefficient of variation using EWMA charts. J Qual Technol 43(3):249–265Google Scholar
  5. 5.
    Castagliola P, Zhang Y, Costa A, Maravelakis P (2012) The variable sample size \(\bar {X}\) chart with estimated parameters. Qual Reliab Eng Int 28(7):687–699CrossRefGoogle Scholar
  6. 6.
    Castagliola P, Achouri A, Taleb H, Celano G, Psarakis S (2013a) Monitoring the coefficient of variation using a variable sampling interval control chart. Qual Reliab Eng Int 29(8):1135–1149CrossRefGoogle Scholar
  7. 7.
    Castagliola P, Achouri A, Taleb H, Celano G, Psarakis S (2013b) Monitoring the coefficient of variation using control charts with run rules. Qual Technol Quant Manag 10(1):75–94Google Scholar
  8. 8.
    Castagliola P, Celano G, Fichera S, Nenes G (2013c) The variable sample size t control chart for monitoring short production runs. Int J Adv Manuf Technol 66(9):1353–1366Google Scholar
  9. 9.
    Costa A (1994) \(\bar {X}\) charts with variable sample size. J Qual Technol 26(3):155–163Google Scholar
  10. 10.
    Hong E, Kang C, Baek J, Kang H (2008) Development of CV control chart using EWMA technique. J Soc Korea Ind Syst Eng 31(4):114–120Google Scholar
  11. 11.
    Iglewicz B, Myers R, Howe R (1968) On the percentage points of the sample coefficient of variation. Biometrika 55(3):580–581CrossRefGoogle Scholar
  12. 12.
    Kang C, Lee M, Seong Y, Hawkins D (2007) A control chart for the coefficient of variation. J Qual Technol 39(2):151–158Google Scholar
  13. 13.
    Latouche G, Ramaswami V (1999) Introduction to matrix analytic methods in stochastic modelling. ASA SIAMGoogle Scholar
  14. 14.
    Neuts M (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. Dover Publications IncGoogle Scholar
  15. 15.
    Reed G, Lynn F, Meade B (2002) Use of coefficient of variation in assessing variability of quantitative assays. Clin Diagn Lab Immunol 9(6):1235–1239Google Scholar
  16. 16.
    Reynolds M (1996) Variable sampling-interval control charts with sampling at fixed times. IIE Trans 28:497–510CrossRefGoogle Scholar
  17. 17.
    Sharpe W (1994) The sharpe ratio. J Portf Manag 21(1):49–58CrossRefGoogle Scholar
  18. 18.
    Tagaras G (1998) A survey of recent developments in the design of adaptive control charts. J Qual Technol 30(3):212–223Google Scholar
  19. 19.
    Wu S (2011) Optimal inspection policy for three-state systems monitored by variable sample size control charts. Int J Adv Manuf Technol 55(5–8):689–697CrossRefGoogle Scholar
  20. 20.
    Zimmer L, Montgomery D, Runger G (1998) Evaluation of the three-state adaptive sample size \(\bar {X}\) control chart. Int J Prod Res 36:733–743MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Philippe Castagliola
    • 1
  • Ali Achouri
    • 2
  • Hassen Taleb
    • 3
  • Giovanni Celano
    • 4
  • Stelios Psarakis
    • 5
  1. 1.IRCCyN UMR CNRS 6597LUNAM Université, Université de NantesNantesFrance
  2. 2.Institut Suprieur de GestionUniversit de TunisTunisTunisia
  3. 3.Higher Institute of Business Administration of GafsaUniversity of GafsaGafsaTunisia
  4. 4.Department of Industrial EngineeringUniversity of CataniaCataniaItaly
  5. 5.Athens University of Economics and BusinessAthensGreece

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