Nonparametric control charts based on runs and Wilcoxon-type rank-sum statistics

In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length ( ARL) are all de...

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Bibliographic Details
Published in:Journal of statistical planning and inference 2009-09, Vol.139 (9), p.3177-3192
Main Authors: Balakrishnan, N., Triantafyllou, I.S., Koutras, M.V.
Format: Article
Language:English
Subjects:
Applications
Average run length
Distribution theory
Distribution-free control charts
Exact sciences and technology
Exceedance statistics
General topics
Lehmann alternatives
Mathematics
Nonparametric methods
Parametric inference
Probability and statistics
Probability theory and stochastic processes
Reliability, life testing, quality control
Sciences and techniques of general use
Shewhart [formula omitted]-chart
Statistical process control
Statistics
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Summary:In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length ( ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate ( FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations.
ISSN:0378-3758
1873-1171
DOI:10.1016/j.jspi.2009.02.013