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A class of distribution-free control charts

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Abstract:

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.

Keywords: Average run length; Estimated control limits; False alarm rate; Nonparametric methods; Order statistics; Precedence statistics; Quantiles; Shewhart X -chart; Statistical process control

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1467-9876.2004.0d489.x

Affiliations: 1: 1University of Alabama, Tuscaloosa, USA 2: 2Eindhoven University of Technology, the Netherlands

Publication date: August 1, 2004

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