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Statistical Papers

, Volume 52, Issue 4, pp 799–811 | Cite as

A unification and some corrections to Markov chain approaches to develop variable ratio sampling scheme control charts

  • Alireza Faraz
  • Erwin SanigaEmail author
Regular Article

Abstract

We provide some unifying definitions, make some corrections to articles by Faraz and Parsian (J Stat Pap 47:569–593, 2006) and Costa (J Qual Technol 26:155–163, 1994; 29:197–204, 1997), and using these provide more accurate tables of results and comparisons of control charts. We also investigate the impact of an incorrectly specified process shift on signal frequency.

Keywords

Quality control charts Variable sample size (VSS) Variable sampling intervals (VSI) Variable sample size and sampling intervals (VSSVSI) Markov chain Adjusted average time to signal (AATS) 

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References

  1. Costa AFB (1994) \({\bar {X}}\) charts with variable sampling size. J Qual Technol 26: 155–163Google Scholar
  2. Costa AFB (1997) \({\bar {X}}\) charts with variable sampling size and sampling intervals. J Qual Technol 29: 197–204Google Scholar
  3. Costa AFB (1999) Joint \({\bar {X}}\) and R charts with variable sample sizes and sampling intervals. J Qual Technol 31: 387–397Google Scholar
  4. Daudin JJ (1992) Double sampling \({\bar {X}}\) charts. J Qual Technol 24: 78–87Google Scholar
  5. Faraz A, Parsian A (2006) Hotelling’s T2 control chart with double warning lines. J Stat Pap 47: 569–593MathSciNetzbMATHCrossRefGoogle Scholar
  6. Prabhu SS, Montgomery DC, Runger GC (1994) A combined adaptive sample size and sampling interval \({\bar {X}}\) control scheme. J Qual Technol 26: 164–176Google Scholar
  7. Reynolds MR Jr, Arnold JC (1989) Optimal one-sided Shewhart control charts with variable sampling intervals. Seq Anal 8: 51–77MathSciNetzbMATHCrossRefGoogle Scholar
  8. Runger GC, Pignatiello JJ (1991) Adaptive sampling for process controls. J Qual Technol 23: 135–155Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Industrial Engineering Department, School of EngineeringTarbiat Modares UniversityTehranIran
  2. 2.Department of Business AdministrationUniversity of DelawareNewarkUSA

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