Log in

On the properties of the hotelling’s T2 control chart with variable sampling intervals

  • Published:
Quality & Quantity Aims and scope Submit manuscript

Abstract

When T 2 control chart is used to monitor a process, it is usually assumed that the samples of size n 0 is taken at constant intervals t 0 . In this paper, we investigate the T 2 control chart for monitoring the process mean vector when the sampling intervals are variable. Recent studies have shown that the variable sampling interval (VSI) scheme helps practitioners detect process shifts more quickly than the classical scheme Fixed Ratio Sampling (FRS). In this paper, it is assumed that the length of time the process remains in control is exponentially distributed.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Alt, F.B.: Multivariate quality control: state of the art. In: ASQC Quality Congress Transactions, pp. 886–893. (1982)

  • Alt F.B.: Multivariate quality control: state of the art. In: Kotz, S., Johnson, N.L. (eds) Encyclopedia of statistical science, vol. 6, pp. 110–122. Wiley, New York (1985)

    Google Scholar 

  • Andrade J.M., Muniategui S., Prada D.: Use of multivariate techniques in quality control of kerosene production. Fuel 76(1), 51–59 (1997)

    Article  Google Scholar 

  • Aparisi F., Haro C.L.: Hotelling’s T 2 control chart with variable sampling intervals. Int. J. Prod. Res. 39(14), 3127–3140 (2001)

    Article  Google Scholar 

  • Bai D.S., Lee K.T.: Variable sampling interval \({\bar{{X}}}\) control charts with an improved switching rule. Int. J. Prod. Econ. 76, 189–199 (2002)

    Article  Google Scholar 

  • Chengalur I.N., Arnold J.C., Reynolds M.R. Jr: Variable sampling intervals for multi parameter Shewhart charts. Commun. Stat.: Theory Method 18, 1769–1792 (1989)

    Article  Google Scholar 

  • Colon H.I.E., Gonzalez Barreto D.R.: Component registration diagnosis for printed circuit boards using process-oriented basis elements. Comp. Ind. Eng. 33(1/2), 389–392 (1997)

    Article  Google Scholar 

  • Costa A.F.B.: \({\bar{{X}}}\) charts with variable sample size and sampling intervals. J. Qual. Technol. 29(2), 197–204 (1997)

    Google Scholar 

  • Cui R., Reynolds M.R. Jr: \({\bar{{X}}}\)-charts with runs rules and variable sampling intervals. Commun. Stat.: Simul. Comput. 17, 1073–1093 (1988)

    Article  Google Scholar 

  • Hatton M.B.: Effective use multivariate control charts. Research publication GMR-4513, General Motors Research Lab, Warren, MI (1983)

    Google Scholar 

  • 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 

  • Jackson J.E.: Multivariate quality control. Commun. Stat. 14(11), 2657–2688 (1985)

    Article  Google Scholar 

  • Kourti T., MacGregore J.F.: Multivariate SPC methods for process and products monitoring. J. Qual. Technol. 28(4), 409–428 (1996)

    Google Scholar 

  • Majcen N., Rius F.X., Zupan J.: Linear and non-linear multivariate analysis in the quality control of industrial dioxide white pigment. Anal. Chim. Acta 348, 87–100 (1997)

    Article  Google Scholar 

  • Mason R.L., Young J.C.: Multivariate Statistical Process Control with Industrial Applications. ASA-SIAM, Philadelphia, PA (2002)

    Book  Google Scholar 

  • Nijhius A., deJong S., Vandeginste B.G.M.: Multivariate statistical process control in chromatography. Chemom. Intell. Lab. Syst. 38(1), 51–62 (1997)

    Article  Google Scholar 

  • Reynolds M.R. Jr, Arnold J.C.: Optimal one-sided Shewhart control charts with variable sampling intervals. Seq. Anal. 8, 51–77 (1989)

    Article  Google Scholar 

  • Reynolds M.R. Jr, Arnold J.C.: Variable sampling intervals \({\bar{{X}}}\) charts in the presence of correlation. J. Qual. Technol. 28(2), 12–30 (1996)

    Google Scholar 

  • Runger G.C., Pignatiello J.J.: Adaptive sampling for process controls. J. Qual. Technol. 23, 135–155 (1991)

    Google Scholar 

  • Runger G.C., Montgomery D.C.: Adaptive sampling enhancements for Shewhart control charts. IIE Transac. 25, 41–51 (1993)

    Article  Google Scholar 

  • Ryan T.P.: Statistical Methods for Quality Improvement. Willey, INC, New York (2000)

    Google Scholar 

  • Sullivan J.H., Woodall W.H.: A comparison of multivariate control charts for individual observations. J. Qual. Technol. 34, 260–276 (1996)

    Google Scholar 

  • Sullivan J.H., Woodall W.H.: Adapting control charts for the preliminary analysis of multivariate observations. Commun. Stat.-Simul. Comput. 27, 953–979 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alireza Faraz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Faraz, A., Chalaki, K. & Moghadam, M.B. On the properties of the hotelling’s T2 control chart with variable sampling intervals. Qual Quant 45, 579–586 (2011). https://doi.org/10.1007/s11135-010-9314-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11135-010-9314-z

Keywords

Navigation