ENBIS-8 in Athens

21 – 25 September 2008 Abstract submission: 14 March – 11 August 2008

A nonparametric control chart based on Wilcoxon rank sum statistic

23 September 2008, 15:00 – 15:20

Abstract

Submitted by
Ioannis Triantafyllou
Authors
I.S. Triantafyllou, N. Balakrishnan, M.V. Koutras
Abstract
Statistical process control is widely used to monitor the quality of a process or of the final product of it. Control charts help the practitioners to identify assignable causes so that the state of statistical control can be achieved. Intuitively, in the event of having an undesirable shift in the process, a control chart should detect it as quickly as possible and give an out-of-control signal. In this article, we introduce a new Wilcoxon-type rank sum control chart, which due to its nonparametric nature does not require the assumption of any specific probability distribution for the underlying process(measurements). More specifically, while the process is in-control, a reference sample is taken from it and the LCL and UCL of the control chart is determined by exploiting appropriate order statistics of the reference sample. Then, test samples are drawn independently of each other (and also of the reference sample) and the decision whether the process remains in-control or not, is based on the sum of the ranks of the test sample observations which lie between the control limits. Exact formulae for the alarm rate, the run length distribution and the average run length (ARL) are all derived. Tables are provided for the implementation of the chart for some typical false alarm rates and numerical comparisons are presented between it and other non-parametric Shewhart-type charts.
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