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An ARL-Unbiased n p -Chart

An ARL-Unbiased n p -Chart Abstract We usually assume that counts of nonconforming items have a binomial distribution with parameters ( n , p ), where n and p represent the sample size and the fraction nonconforming, respectively. The non-negative, discrete and usually skewed character and the target mean ( n p 0 ) ${(np_0)}$ of this distribution may prevent the quality control engineer to deal with a chart to monitor p with: a pre-specified in-control average run length (ARL), say α - 1 ${\alpha ^{-1}}$ ; a positive lower control limit; the ability to control not only increases but also decreases in p in an expedient fashion. Furthermore, as far as we have investigated, the n p - and p -charts proposed in the Statistical Process Control literature are ARL-biased, in the sense that they take longer, in average, to detect some shifts in the fraction nonconforming than to trigger a false alarm. Having all this in mind, this paper explores the notions of uniformly most powerful unbiased tests with randomization probabilities to eliminate the bias of the ARL function of the n p -chart and to bring its in-control ARL exactly to α - 1 ${\alpha ^{-1}}$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Economic Quality Control de Gruyter

An ARL-Unbiased n p -Chart

Economic Quality Control , Volume 31 (1) – Jun 1, 2016

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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
0940-5151
eISSN
1869-6147
DOI
10.1515/eqc-2015-0013
Publisher site
See Article on Publisher Site

Abstract

Abstract We usually assume that counts of nonconforming items have a binomial distribution with parameters ( n , p ), where n and p represent the sample size and the fraction nonconforming, respectively. The non-negative, discrete and usually skewed character and the target mean ( n p 0 ) ${(np_0)}$ of this distribution may prevent the quality control engineer to deal with a chart to monitor p with: a pre-specified in-control average run length (ARL), say α - 1 ${\alpha ^{-1}}$ ; a positive lower control limit; the ability to control not only increases but also decreases in p in an expedient fashion. Furthermore, as far as we have investigated, the n p - and p -charts proposed in the Statistical Process Control literature are ARL-biased, in the sense that they take longer, in average, to detect some shifts in the fraction nonconforming than to trigger a false alarm. Having all this in mind, this paper explores the notions of uniformly most powerful unbiased tests with randomization probabilities to eliminate the bias of the ARL function of the n p -chart and to bring its in-control ARL exactly to α - 1 ${\alpha ^{-1}}$ .

Journal

Economic Quality Controlde Gruyter

Published: Jun 1, 2016

References