Advertisement

Statistical Design of Attribute Charts for Monitoring and Continuous Improvement When Count Levels Are Low

  • Erwin M. Saniga
  • Darwin J. Davis
  • James M. Lucas
Conference paper
Part of the Frontiers in Statistical Quality Control book series (FSQC, volume 7)

Abstract

Consider the situation where an attribute chart is being used to monitor a process for special causes of variability and attempts at continuous improvement are being made. In certain cases where the count level is low no lower control limit will exist for standard Shewhart control charts.

Optimal methods for shift detection when attribute data is being used are traditional CUSUM methods but CUSUM methods have not enjoyed wide popularity when compared to Shewhart methods because they are difficult to apply and understand.

In this paper we show how one can design special CUSUMs that will enable the Shewhart attribute chart user to monitor decreases in the process parameter when count levels are small. These CUSUMs, like the Shewhart chart, are easy to understand, easy to use, and, with the application of the algorithm given in this paper, easy to design.

A comparison with traditional CUSUMs is given and a variety of example designs developed using this algorithm are presented.

Keywords

Control Chart High Side CUSUM Chart Statistical Quality Control Lower Control Limit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Acosta-Mejia, C.A. (1999) Improved p Charts to Monitor Process Quality. IIE Transactions 31, 509–516Google Scholar
  2. 2.
    Bourke, P.D. (2001) Sample Size and the Binomial CUSUM Control Chart: The Case of 100% Inspection. Metrika 53, 51–70CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Brook, D., Evans, D.A. (1972) An Approach to the Probability Distribution of CUSUM Run Length. Biometrika 59, 539–549CrossRefMATHMathSciNetGoogle Scholar
  4. 5.
    Gan, F.F. (1993) An Optimum Design of CUSUM Control Charts for Binomial Counts. Journal of Applied Statistics 11, 16–31Google Scholar
  5. 6.
    Lucas, J.M. (1989) Control Schemes for Low Level Counts. Journal of Quality Technology 21, 199–201Google Scholar
  6. 7.
    Lucas, J.M. (1985) Counted Data CUSUMS. Technometrics 27, 129–144CrossRefMATHMathSciNetGoogle Scholar
  7. 8.
    Moustakides, G.V. (1986) Optimal Stopping Times for Detecting Changes in Distributions. The Annals of Statistics 14, 1379–1387CrossRefMATHMathSciNetGoogle Scholar
  8. 9.
    Nelson, L.S. (1997) Supplementary Runs Tests for np Charts. Journal of Quality Technology 29, 225–277Google Scholar
  9. 10.
    Page, E.S. (1955) Control Charts with Warning Lines. Biometrika 42, 243–257MATHMathSciNetGoogle Scholar
  10. 11.
    Reynolds, M.R., Jr., Stoumbos, Z.G. (1999) A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously. Journal of Quality Technology 31, 87–105Google Scholar
  11. 12.
    Reynolds, M.R., Jr., Stoumbos, Z.G. (2000) A General Approach to Modeling CUSUM Charts for a Proportion. HE Transactions 32, 515–535Google Scholar
  12. 13.
    Reynolds, M.R., Jr., Stoumbos, Z.G. (2001) Monitoring a Proportion Using CUSUM and SPRT Control Charts. Frontiers in Statistical Quality Control 6, 155–175CrossRefGoogle Scholar
  13. 14.
    Ryan, T.P. (1989) Statistical Methods for Quality Improvement. Wiley, New YorkGoogle Scholar
  14. 15.
    Saniga, E.M., Davis, D.J., McWilliams, T.P. (1995) Economic, Statistical, and Economic Statistical Design of Attribute Charts. Journal of Quality Technology 27, 56–73Google Scholar
  15. 16.
    Schwertman, N.C., Ryan, T.P. (1997) Implementing Optimal Attribute Control Charts. Journal of Quality Technology 29, 99–104Google Scholar
  16. 17.
    Shore, H. (2000) General Control Charts for Attributes. IIE Transactions 32, 1149–1160Google Scholar
  17. 18.
    Woodall, W.H. (1985) The Statistical Design of Quality Control Charts. The Statistician 34, 155–160CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Erwin M. Saniga
    • 1
  • Darwin J. Davis
    • 1
  • James M. Lucas
    • 2
  1. 1.University of DelawareUSA
  2. 2.J. M. Lucas and AssociatesUSA

Personalised recommendations