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Chakraborti, S.; van der Laan, P.; van de Wiel, M. A.

A class of distribution-free control charts. (English) Zbl 1111.62386

J. R. Stat. Soc., Ser. C, Appl. Stat. 53, No. 3, 443-462 (2004).
Summary: A class of Shewhart-type distribution-free control charts is considered. A key advantage of these charts is that the in-control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart X-chart. A numerical illustration is given.

Cited in 1 Review
Cited in 36 Documents

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62G99 Nonparametric inference

Software:

Mathematica
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Full Text: DOI

References:

[1] Amin R., Communs Statist. Theory Meth. 24 pp 1597– (1995)
[2] Chakraborti S., Communs Statist. Simuln Computn 29 pp 61– (2000)
[3] Chakraborti S., Statistician 45 pp 351– (1996)
[4] Chakraborti S., Biometr. J. 39 pp 99– (1997)
[5] Chakraborti S., J. Qual. Technol. 33 pp 304– (2001)
[6] Chakraborti S., Statistics, Probability and Operations Research Report 2000-11 (2000)
[7] Gibbons J. D., Nonparametric Statistical Inference (2003) · Zbl 1115.62004
[8] DOI: 10.1111/1467-9884.00056 · doi:10.1111/1467-9884.00056
[9] Mathisen H. C., Ann. Math. Statist. 14 pp 188– (1943)
[10] Montgomery D. C., Introduction to Statistical Quality Control (1997) · Zbl 0997.62503
[11] Nelson L. S., Technometrics 5 pp 491– (1963)
[12] Nelson L. S., J. Qual. Technol. 25 pp 140– (1993)
[13] C. P. Quesenberry (1993 ) The effect of sample size on estimated control limits for andXcontrol charts . , 25 , 237 -247 .
[14] Wolfram S., The Mathematica Book (1996)
[15] Woodall W. H., J. Qual. Technol. 31 pp 376– (1999)
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