Skip to main content
Log in

Monitoring kth order runs in binary processes

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

An Erratum to this article was published on 13 June 2012

Abstract

Procedures for continuously monitoring binary attribute data processes are of utmost relevance for fields like electrical engineering, chemical production, software quality engineering, healthcare monitoring, and many more. In this article, new approaches are proposed, where kth order runs in a binary process are monitored. We derive methods for evaluating the performance of the new control charts, discuss computational issues of these methods and give design recommendations for the control charts. A real-data example demonstrates the successful application of the new control procedures.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aki S, Hirano K (1993) Discrete distributions related to succession events in a two-state Markov chain. In: Matusita K et al. (eds) Statistical science and data analysis, pp. 467–474

  • Bourke PD (1991) Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. J Qual Technol 23(3): 225–238

    Google Scholar 

  • Brook D, Evans DA (1972) An approach to the probability distribution of cusum run length. Biometrika 59(3): 539–549

    Article  MathSciNet  MATH  Google Scholar 

  • Cantell BS, Collica R, Ramirez JG (1998) Statistical process monitoring of correlated binary and count data using mixture distributions. In: Statistics, data analysis, and modeling, SAS conference proceedings: SAS Users Group International 23, Nashville

  • Feller W (1968) An introduction to probability theory and its applications, vol 1, 3rd edn. Wiley, New York, London

    Google Scholar 

  • Godbole AP (1990) Specific formulae for some success run distributions. Stat Probab Lett 10: 119–124

    Article  MathSciNet  MATH  Google Scholar 

  • Hart MK, Lee KY, Hart RF, Robertson JW (2003) Application of attribute control charts to risk-adjusted data for monitoring and improving health care performance. Qual Manag Health Care 12(1): 5–19

    Article  Google Scholar 

  • Hubbard MR (2003) Statistical quality control for the food industry, 3rd edn. Springer Verlag, New York

    Book  Google Scholar 

  • Kan SH (2003) Metrics and models in software quality engineering, 2nd edn. Addison-Wesley, Reading

    Google Scholar 

  • Knoth S (2006) The art of evaluating monotoring schemes—how to measure the performance of control charts?. In: Lenz HJ, Wilrich PT (eds) Frontiers in statistical quality control, vol 8. Physica Verlag, Heidelberg, pp 74–99

    Chapter  Google Scholar 

  • Montgomery DC (2005) Introduction to statistical quality control, 5th edn. Wiley, Newyork

    MATH  Google Scholar 

  • Mousavi S, Reynolds MR Jr (2009) A CUSUM chart for monitoring a proportion with autocorrelated binary observations. J Qual Technol 41(4): 401–414

    Google Scholar 

  • Philippou AN, Georghiou C, Philippou GN (1983) A generalized geometric distribution and some of its properties. Stat Probab Lett 1: 171–175

    Article  MathSciNet  MATH  Google Scholar 

  • Quesenberry CP (1995) Geometric Q charts for high quality processes. J Qual Technol 27(4): 304–315

    Google Scholar 

  • Reynolds MR Jr, Stoumbos ZG (1999) A CUSUM chart for monitoring a proportion when inspecting continuously. J Qual Technol 31(1): 87–108

    Google Scholar 

  • Shmueli G, Cohen A (2000) Run-related probability functions applied to sampling inspection. Technometrics 42(2): 188–202

    Article  Google Scholar 

  • Shmueli G, Cohen A (2003) Run-length distribution for control charts with runs and scans rules. Commun Stat Theory Methods 32(2): 475–495

    Article  MathSciNet  MATH  Google Scholar 

  • Spliid H (2010) An exponentially weighted moving average control chart for Bernoulli data. Qual Reliab Eng Int 26(1): 97–113

    Article  Google Scholar 

  • Tsai C-F (2002) The genetic algorithm-based system for economic design of multiple control charts. Chung Hua J Manag 3(3): 103–116

    Google Scholar 

  • Walters K, Bristol K, Hart P, Fischbeck K, Dimock F, LeMieux P, Worsley C (2002) Improving the reflow process with SPC: part 2. Circuits Assembly January:2–5

  • Weiß CH (2009) Group inspection of dependent binary processes. Qual Reliab Eng Int 25(2): 151–165

    Article  Google Scholar 

  • Weiß CH (2012) Continuously monitoring categorical processes. Qual Technol Quant Mana 9(2): 581–598

    Google Scholar 

  • Weiß CH, Atzmüller M (2010) EWMA control charts for monitoring binary processes with applications to medical diagnosis data. Qual Reliab Eng Int 26(8): 795–805

    Article  Google Scholar 

  • Woodall WH (1997) Control charts based on attribute data: bibliography and review. J Qual Technol 29(2): 172–183

    Google Scholar 

  • Xie M, Goh N, Kuralmani V (2000) On optimal setting of control limits for geometric chart. Int J Reliab Qual Safety Eng 7(1): 17–25

    Article  Google Scholar 

  • Zhang L, Govindaraju K, Bebbington M, Lai CD (2004) On the statistical design of geometric control charts. Qual Technol Quant Manag 1(2): 233–243

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Christian H. Weiß.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weiß, C.H. Monitoring kth order runs in binary processes. Comput Stat 28, 541–562 (2013). https://doi.org/10.1007/s00180-012-0316-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-012-0316-2

Keywords

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy