The optimization of a statistical process control with a variable sampling interval is studied. A control performance index is the expected loss, caused by delay in detecting process change. It is to be minimized by a proper choice of a sampling interval. The mathematical model of this problem is a nonstandard variational calculus problem with two types of constraints, an isoperimetric constraint and two geometric constraints. The integrands in the cost functional and the isoperimetric constraint are independent of the derivative of the minimizing function. Therefore, the classical Euler-Lagrange equation approach is not applicable when analyzing this extremal problem. The optimization problem depends on the signal-to-noise ratio parameter. The original problem is transformed to an equivalent optimal control problem. Based on the value of the parameter, the latter is decomposed into two simpler problems, solved by application of Pontryagin’s Maximum Principle. The theoretical results are evaluated by numerical simulations.
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ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 12–15, 2012
Chicago, Illinois, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-4502-8
PROCEEDINGS PAPER
Application of Pontryagin’s Maximum Principle to Statistical Process Control Optimization Available to Purchase
Valery Y. Glizer,
Valery Y. Glizer
Ort Braude College, Karmiel, Israel
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Vladimir Turetsky,
Vladimir Turetsky
Ort Braude College, Karmiel, Israel
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Emil Bashkansky
Emil Bashkansky
Ort Braude College, Karmiel, Israel
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Valery Y. Glizer
Ort Braude College, Karmiel, Israel
Vladimir Turetsky
Ort Braude College, Karmiel, Israel
Emil Bashkansky
Ort Braude College, Karmiel, Israel
Paper No:
DETC2012-70104, pp. 813-822; 10 pages
Published Online:
September 9, 2013
Citation
Glizer, VY, Turetsky, V, & Bashkansky, E. "Application of Pontryagin’s Maximum Principle to Statistical Process Control Optimization." Proceedings of the ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 3: 38th Design Automation Conference, Parts A and B. Chicago, Illinois, USA. August 12–15, 2012. pp. 813-822. ASME. https://doi.org/10.1115/DETC2012-70104
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