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Monitoring k ‐step‐ahead Controlled Processes
Author(s) -
Nugent Edward,
BaykalGürsoy Melike,
Gürsoy Kemal
Publication year - 2005
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.608
Subject(s) - control chart , process (computing) , variance (accounting) , independent and identically distributed random variables , statistical process control , chart , controller (irrigation) , control limits , control theory (sociology) , computer science , process control , control (management) , engineering , reliability engineering , statistics , mathematics , random variable , artificial intelligence , business , biology , operating system , accounting , agronomy
A dynamical system controlled by a k ‐step‐ahead minimum variance controller is considered. Independent, identically distributed one‐step‐ahead process residuals are given for use in statistical process monitoring schemes. Problems encountered in the application of the monitoring schemes are discussed, particularly with respect to detecting process upsets. Upsets may occur in any of three ways, for which expressions are derived. It is shown that the mechanism by which upsets occur influences the ability of the residuals to detect the upsets. It is also shown that the effect of the disturbance on the residuals is independent of the process time delay k . The ability of the residuals to detect a change in the process dispersion is discussed. It is shown that the disturbance dynamics do not alter this ability. This information is useful in obtaining accurate estimates of control chart performance and directing the statistical process control practitioner in modifying the control chart design. Copyright © 2004 John Wiley & Sons, Ltd.