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The Efficiency of a Wavelet Transformation Approach to Prospective Monitoring
Author(s) -
Steward Robert M.,
Rigdon Steven E.
Publication year - 2015
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1607
Subject(s) - control chart , wavelet , statistical process control , transformation (genetics) , bayesian probability , change detection , computer science , process (computing) , wavelet transform , false alarm , constant false alarm rate , point (geometry) , statistics , algorithm , artificial intelligence , mathematics , biochemistry , chemistry , gene , operating system , geometry
We prospectively monitor a stochastic process x 1 , x 2 , … in an effort to detect quickly some statistical change to the process mean. Initially, the process is monitored with a classic control chart equipped with statistical control limits indicating the process is in control or signaling an alarm sometime after a statistical change occurs. Once the alarm signals, we would then like to ‘look back’ and determine at which point the process changed. To this end, we apply and compare three change‐point detection methods under a variety of different assumptions. In particular, two classic methods of Bayesian and maximum likelihood estimation change‐point detection are compared with a technique that first applies the discrete wavelet transform to the series and then applies Bayesian methods directly to the wavelet details. Copyright © 2013 John Wiley & Sons, Ltd.