Skip to main content

The Effect of Non-Normality on the Performance of CUSUM Procedures

  • Conference paper
Frontiers in Statistical Quality Control 6

Part of the book series: Frontiers in Statistical Quality Control ((FSQC,volume 6))

Abstract

Cumulative sum (CUSUM) procedures have been used by many practitioners as an alternative to a Shewhart chart. The value of normality-based CUSUM procedures is well-established and CUSUM procedures have been used for decades. In recent years CUSUM procedures have also been proposed for random variables with non-normal distributions (see, e.g., Lucas [16, 17], Wang [32], Gan [8, 9], Radaelli [26], Mathers, Harris, and Lancaster [21], and Edgeman [6]

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Amin, R.W., M. R. Reynolds, Jr., and S. Bakir (1995) Nonparametric control charts based upon the sign statistic. Communications in Statistics - Theory and Methods 24 1597–1623

    Article  MATH  MathSciNet  Google Scholar 

  2. Box, G. E. P. and A. Luceño (1997) Statistical Control by Monitoring and Feedback Adjustment. New York: Wiley

    MATH  Google Scholar 

  3. Brook, D. and D. A. Evans (1972) An approach to the probability distribution of CUSUM run length. Biometrika 59(3), 539–549

    Article  MATH  MathSciNet  Google Scholar 

  4. Champ, C. W. and S. E. Rigdon (1991) A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts. Communications in Statistics — Simulation and Computation 20(1), 191–204

    Article  MATH  Google Scholar 

  5. Desmond, A. F. and G. R. Chapman (1993) Modeling task completion data with inverse Gaussian mixtures.Applied Statistics 42(4), 603–613

    Article  Google Scholar 

  6. Edgeman, R. L. (1996) SPRT and CUSUM results for inverse Gaussian processes. Communications in Statistics — Theory and Methods 25(11), 2797–2806

    Article  MATH  Google Scholar 

  7. Faddy, B. J. (1996) The Effect of Non-Normality on the Performance of Cumulative Sum Quality Control Schemes. Honours Thesis, Department of Statistics, University of Newcastle, Australia

    Google Scholar 

  8. Gan, F. F. (1993) An optimal design of CUSUM control charts for binomial counts. Journal of Applied Statistics 20, 445–460

    Article  Google Scholar 

  9. Gan, F. F. (1994) Design of optimal exponential CUSUM control charts. Journal of Quality Technology 26 109–124

    Google Scholar 

  10. Geary, R.C. (1942) Testing for normality. Biometrika 34 209–242

    MathSciNet  Google Scholar 

  11. Hawkins, D. M. (1993) Robustification of cumulative sum charts by Winsorization. Journal of Quality Technology 25, 248–261

    Google Scholar 

  12. Hawkins, D. M. and D. H. Olwell (1997) Inverse Gaussian cumulative sum control charts for location and shape. The Statistician 46(2), 323–335

    Google Scholar 

  13. Hawkins, D. M. and D. H. Olwell (1998) Cumulative Sum Charts and Charting for Quality Improvement. New York: Springer-Verlag

    Book  MATH  Google Scholar 

  14. Kemp, K. W. (1967) An example of errors incurred by erroneously assuming normality for Cusum schemes. Technometrics 9 457–464

    Article  MathSciNet  Google Scholar 

  15. Lucas, J. M. (1982) Combined Shewhart-CUSUM quality control schemes. Journal of Quality Technology 8(1) 1–12

    Google Scholar 

  16. Lucas, J. M. (1985) Counted data CUSUMs. Technometrics 27 129–144

    Article  MATH  MathSciNet  Google Scholar 

  17. Lucas, J. M. (1989) Control schemes for low count levels. Journal of Quality Technology 21199–201

    Google Scholar 

  18. Lucas, J. M. and R. B. Crosier (1982a) Fast Initial Response for CUSUM quality control schemes: Give your CUSUM a head start. Technometrics 24(3), 199–205

    Article  Google Scholar 

  19. Lucas, J. M. and R. B. Crosier (1982b) Robust CUSUM. Communications in Statistics — Theory and Methods 11 2669–2687

    Article  MATH  MathSciNet  Google Scholar 

  20. Lucas, J. M. and M. S. Saccucci (1990) Exponentially weighted moving average control schemes: properties and enhancements (with discussion). Technometrics 32 1–29

    Article  MathSciNet  Google Scholar 

  21. Mathers, C. D., R. S. Harris, and P. A. L. Lancaster (1994) A cusum scheme based on the exponential distribution for surveillance of rare congenital malformations. Australian Journal of Statistics 36 21–30

    Article  Google Scholar 

  22. Montgomery, D. C. (1996) Introduction to Statistical Quality Control, 3rd edition. New York: Wiley

    Google Scholar 

  23. Moore, P. G. (1957) Normality in quality control charts. Applied Statistics 6(3), 171–179

    Article  Google Scholar 

  24. Nester, M. (1996) An applied statistician’s creed. Applied Statistics 45(4), 401–410

    Article  MathSciNet  Google Scholar 

  25. Quesenberry, C. P. (1993) The effect of sample size on estimated limits for X and X control charts. Journal of Quality Technology 25(4), 237–247

    Google Scholar 

  26. Radaelli, G. (1994) Poisson and negative binomial dynamics for counted data under CUSUM-type charts. Journal of Applied Statistics 21, 347–356

    Article  Google Scholar 

  27. Ryan, T. P. (1989)Statistical Methods for Quality Improvement. New York: Wiley

    Google Scholar 

  28. Ryan, T. P. (1997) “Individual contribution” to: A discussion of statistically-based process monitoring and control. Journal of Quality Technology 29 150–151

    Google Scholar 

  29. Schilling, E. G. and P. R. Nelson (1976) The effect of non-normality on the control limits of X-charts. Journal of Quality Technology 8(4), 183–188

    Google Scholar 

  30. Tweedie, M. C. K. (1957) Statistical properties of inverse Gaussian distributions, I. Annals of Mathematical Statistics [28 362–377

    Article  MATH  MathSciNet  Google Scholar 

  31. Van Dobben de Bruyn, C.S. (1968) Cumulative Sum Tests: Theory and Practice. Griffin’s Statistical Monographs and Courses No. 24. New York: Hafner

    Google Scholar 

  32. Wang, A.-L. (1990) Exponential cusum scheme for detecting a decrease in mean. Sankhya, Series B 52 105–114

    MATH  Google Scholar 

  33. Wheeler, D. J. and D. S. Chambers (1986)Understanding Statistical Process Control. Knoxville, TN: SPC Press

    Google Scholar 

  34. Woodall, W. H. (1984) On the Markov chain approach to the two-sided CUSUM procedure. Technometrics 26(1), 41–46

    Article  MATH  Google Scholar 

  35. Yourstone, S. A. and W. J. Zimmer (1992) Non-normality and the design of control charts for averages. Decision Sciences 23 1099–1113

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ryan, T.P., Faddy, B.J. (2001). The Effect of Non-Normality on the Performance of CUSUM Procedures. In: Lenz, HJ., Wilrich, PT. (eds) Frontiers in Statistical Quality Control 6. Frontiers in Statistical Quality Control, vol 6. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57590-7_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-57590-7_11

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1374-6

  • Online ISBN: 978-3-642-57590-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics