Quality & Quantity

, 43:903 | Cite as

Hotelling’s T 2 control chart with two adaptive sample sizes

Orginal Paper


Some quality control schemes have been developed when several related quality characteristics are to be monitored. The familiar multivariate process monitoring and control procedure is the Hotelling’s T 2 control chart for monitoring the mean vector of the process. It is a direct analog of the univariate shewhart \({\bar{x}}\) chart. As in the case of univariate, the ARL improvements are very important particularly for small process shifts. In this paper, we study the T 2 control chart with two-state adaptive sample size, when the shift in the process mean does not occur at the beginning but at some random time in the future. Further, the occurrence time of the shift is assumed to be exponentially distributed random variable.


Hotelling’s T2 control chart Adjusted average time to signal (AATS) Adaptive sample size 


  1. Aparisi F.: Hotelling’s T 2 control chart with adaptive sample sizes. Int. J. Prod. Res. 34(10), 2853–2862 (1996)CrossRefGoogle Scholar
  2. Aparisi F.: Sampling plans for the multivariate T 2 control chart. Qual. Eng. 10, 141–147 (1997)CrossRefGoogle Scholar
  3. Brook D., Evans D.A.: An approach to the probability distribution of CUSUM run length. Biometrika 59, 539–549 (1972)CrossRefGoogle Scholar
  4. Burr I.W.: Control charts for measurements with varying sample sizes. J. Qual. Technol. 1, 163–167 (1969)Google Scholar
  5. Cinlar E.: Introduction to stochastic Process. Prentice Hall, Englewood Cliff NJ (1975)Google Scholar
  6. Costa A.F.B.: \({\bar{x}}\) charts with variable sampling size. J. Qual. Technol. 26, 155–163 (1994)Google Scholar
  7. Costa A.F.B.: \({\bar{x}}\) charts with variable sample size and sampling intervals. J. Qual. Technol. 29, 197–204 (1997)Google Scholar
  8. Daudin J.J.: Double sampling \({\bar{x}}\) charts. J. Qual. Technol. 24, 78–87 (1992)Google Scholar
  9. Hotelling H. : Multivariate quality control. In: Eisenhart, C., Hastay, M., Wallis, W.A. (eds) Techniques of Statistical Analysis, pp. 111–184. McGraw-Hill, New York (1947)Google Scholar
  10. Jackson J.E.: Multivariate quality control. Commun. Stat. 14(11), 2657–2688 (1985)CrossRefGoogle Scholar
  11. Prabhu S.S., Runger G.C., Keats J.B.: \({\bar{x}}\) chart with adaptive sample sizes. Int. J. Prod. Res. 31, 2895–2909 (1993)CrossRefGoogle Scholar
  12. Taam W., Subbaiah P., Liddy W.: A note on multivariate capability indices. J. Appl. Stat. 20(3), 339–351 (1993)CrossRefGoogle Scholar
  13. Zimmer L.S., Montgomery D.C., Runger G.C.: Evaluation of a Three-state adaptive sample size \({\bar{x}}\) control chart. Int. J. Prod. Res. 36, 733–743 (1998)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Industrial Engineering Department, School of EngineeringTarbiat Modares UniversityTehranIran
  2. 2.Department of Statistics, Faculty of EconomicAllameh Tabatabaee UniversityTehranIran

Personalised recommendations