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.
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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
Brook D, Evans DA (1972) An approach to the probability distribution of cusum run length. Biometrika 59(3): 539–549
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
Godbole AP (1990) Specific formulae for some success run distributions. Stat Probab Lett 10: 119–124
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
Hubbard MR (2003) Statistical quality control for the food industry, 3rd edn. Springer Verlag, New York
Kan SH (2003) Metrics and models in software quality engineering, 2nd edn. Addison-Wesley, Reading
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
Montgomery DC (2005) Introduction to statistical quality control, 5th edn. Wiley, Newyork
Mousavi S, Reynolds MR Jr (2009) A CUSUM chart for monitoring a proportion with autocorrelated binary observations. J Qual Technol 41(4): 401–414
Philippou AN, Georghiou C, Philippou GN (1983) A generalized geometric distribution and some of its properties. Stat Probab Lett 1: 171–175
Quesenberry CP (1995) Geometric Q charts for high quality processes. J Qual Technol 27(4): 304–315
Reynolds MR Jr, Stoumbos ZG (1999) A CUSUM chart for monitoring a proportion when inspecting continuously. J Qual Technol 31(1): 87–108
Shmueli G, Cohen A (2000) Run-related probability functions applied to sampling inspection. Technometrics 42(2): 188–202
Shmueli G, Cohen A (2003) Run-length distribution for control charts with runs and scans rules. Commun Stat Theory Methods 32(2): 475–495
Spliid H (2010) An exponentially weighted moving average control chart for Bernoulli data. Qual Reliab Eng Int 26(1): 97–113
Tsai C-F (2002) The genetic algorithm-based system for economic design of multiple control charts. Chung Hua J Manag 3(3): 103–116
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
Weiß CH (2012) Continuously monitoring categorical processes. Qual Technol Quant Mana 9(2): 581–598
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
Woodall WH (1997) Control charts based on attribute data: bibliography and review. J Qual Technol 29(2): 172–183
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
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
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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
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DOI: https://doi.org/10.1007/s00180-012-0316-2