Abstract
Classical control charts are very sensitive to deviations from normality. In this respect, nonparametric charts form an attractive alternative. However, these often require considerably more Phase I observations than are available in practice. This latter problem can be solved by introducing grouping during Phase II. Then each group minimum is compared to a suitable upper limit (in the two-sided case also each group maximum to a lower limit). In the present paper it is demonstrated that such MIN charts allow further improvement by adopting a sequential approach. Once a new observation fails to exceed the upper limit, its group is aborted and a new one starts right away. The resulting CUMIN chart is easy to understand and implement. Moreover, this chart is truly nonparametric and has good detection properties. For example, like the CUSUM chart, it is markedly better than a Shewhart X-chart, unless the shift is really large.
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References
Albers W, KallenbergWCM (2004) Empirical nonparametric control charts: estimation effects and corrections. J Appl Stat 31:345–360
Albers W, Kallenberg WCM (2005a) New corrections for old control charts. Qual Eng 17: 467–473
Albers W, Kallenberg WCM (2005b) Tail behavior of the empirical distribution function of convolutions. Math Methods Stat 14: 133–162
Albers W, Kallenberg WCM (2006) Alternative Shewhart-type charts for grouped observations. Metron LXIV(3): 357–375
Albers W, Kallenberg WCM (2008) Minimum control charts. J Stat Plan Inference 138: 539–551
Albers W, Kallenberg WCM, Nurdiati S (2004) Parametric control charts. J Stat Plan Inference 124: 159–184
Albers W, Kallenberg WCM, Nurdiati S (2006) Data driven choice of control charts. J Stat Plan Inference 136: 909–941
Bakir ST, Reynolds MR Jr (1979) A nonparametric procedure for process control based on within-group ranking. Technometrics 21: 175–183
Bakir ST (2006) Distribution-free quality control charts based on signed-rank-like statistics. Commun Stat Theory Methods 35: 743–757
Chakraborti S, van der Laan P, Bakir ST (2001) Nonparametric control charts: an overview and some results. J Qual Technol 33: 304–315
Chakraborti S, van der Laan P, van de Wiel MA (2004) A class of distribution-free control charts. J Royal Stat Soc Ser C 53: 443–462
Chan LK, Hapuarachchi KP, Macpherson BD (1988) Robustness of \({\overline{X}}\) and R charts. IEEE Trans Reliability 37: 117–123
Hawkins DM, Olwell DH (1998) Cumulative SUM Charts and charting for quality improvement. Springer, New York
Lorden G (1971) Procedures for reacting to a change in distribution. Ann Math Stat 42: 1897–1908
Lucas JM (1982) Combined Shewhart-CUSUM quality control schemes. J Qual Technol 14: 51–59
Page ES (1954) Continuous inspection themes. Biometrika 41: 100–115
Pappanastos EA, Adams BM (1996) Alternative designs of the Hodges–Lehmann control chart. J Qual Technol 28: 213–223
Qiu P, Hawkins D (2001) A rank based multivariate CUSUM procedure. Technometrics 43: 120–132
Qiu P, Hawkins D (2003) A nonparametrice multivariate cumulative sum procedure for detecting shifts in all directions. J Royal Statist Soc, Ser d 52: 151–164
Ross SM (1996) Some results for renewal processes, 2nd edn. Wiley, New York
Ryan TP (1989) Statistical methods for quality improvement. Wiley, New York
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Albers, W., Kallenberg, W.C.M. CUMIN charts. Metrika 70, 111–130 (2009). https://doi.org/10.1007/s00184-008-0184-5
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DOI: https://doi.org/10.1007/s00184-008-0184-5