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Erschienen in:
Use of Conditional False Alarm Metric in Statistical Process Monitoring Kapitel lesen Erstes Kapitel lesen

2021 | OriginalPaper | Buchkapitel

ARL-Unbiased CUSUM Schemes to Monitor Binomial Counts

verfasst von : Manuel Cabral Morais, Sven Knoth, Camila Jeppesen Cruz, Christian H. Weiß

Erschienen in: Frontiers in Statistical Quality Control 13

Verlag: Springer International Publishing

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Abstract

Counted output, such as the number of defective items per sample, is often assumed to have a marginal binomial distribution. The integer and asymmetrical nature of this distribution and the value of its target mean hinders the quality control practitioner from dealing with a chart for the process mean with a pre-stipulated in-control average run length (ARL) and the ability to swiftly detect not only increases but also decreases in the process mean. In this paper we propose ARL-unbiased cumulative sum (CUSUM) schemes to rapidly detect both increases and decreases in the mean of independent and identically distributed as well as first-order autoregressive (AR(1)) binomial counts. Any shift is detected more quickly than a false alarm is generated by these schemes and their in-control ARL coincide with the pre-specified in-control ARL. We use the R statistical software to provide compelling illustrations of all these CUSUM schemes.

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Vorheriges Kapitel An Average Loss Control Chart Under a Skewed Process Distribution
Nächstes Kapitel Statistical Aspects of Target Setting for Attribute Data Monitoring
Fußnoten
1
Notice that the transient states can be ordered as follows: \((0,0), (0,1/b^-), \dots , (0,c^-/b^-),\)
\((1,0), (1,1/b^-), \dots , (1,c^-/b^-),\) \(\dots , (c^+/b^+,0), (c^+/b^+,1), \dots , (c^+/b^+,c^-/b^-)\).
 
2
The transient states can be ordered as follows: \((0, 0,0), (0, 0,1/b^-), \dots , (0, 0,c^-/b^-),\)\((0,1,0), (0,1,1/b^-), \dots , (0,1,c^-/b^-), \dots , (n,c^+/b^+,0), (n, c^+/b^+,1), \dots , (n, c^+/b^+,c^-/b^-)\).
 
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Metadaten
Titel
ARL-Unbiased CUSUM Schemes to Monitor Binomial Counts
verfasst von
Manuel Cabral Morais
Sven Knoth
Camila Jeppesen Cruz
Christian H. Weiß
Copyright-Jahr
2021
Buch
Frontiers in Statistical Quality Control 13

Print ISBN: 978-3-030-67855-5

Electronic ISBN: 978-3-030-67856-2

Copyright-Jahr: 2021

DOI
https://doi.org/10.1007/978-3-030-67856-2_6

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