Authors:
Valery Y. Glizer
and
Vladimir Turetsky
Affiliation:
Department of Applied Mathematics, ORT Braude College of Engineering, P.O.B. 78, Karmiel 2161002 and Israel
Keyword(s):
Statistical Control, Statistical Information, Quadratic Cost Functional, Optimal Time-sampling, Pontryagin’s Maximum Principle, Quadratic Optimization.
Related
Ontology
Subjects/Areas/Topics:
Artificial Intelligence
;
Business Analytics
;
Cardiovascular Technologies
;
Computing and Telecommunications in Cardiology
;
Data Engineering
;
Decision Support Systems
;
Decision Support Systems, Remote Data Analysis
;
Formal Methods
;
Health Engineering and Technology Applications
;
Informatics in Control, Automation and Robotics
;
Intelligent Control Systems and Optimization
;
Knowledge-Based Systems
;
Optimization Algorithms
;
Planning and Scheduling
;
Simulation and Modeling
;
Symbolic Systems
Abstract:
We consider the problem of constructing an optimal time-sampling for a Statistical Process Control (or, briefly, Statistical Control (SC)). The aim of this time-sampling is to minimize the expected loss, caused by a delay in the detection of an undesirable process change. We study the case where this loss is a quadratic functional of the sampling time-interval. This problem is modeled by a nonstandard calculus of variations problem. We propose two approaches to the solution of this calculus of variations problem. The first approach is based on its equivalent transformation to an optimal control problem. The latter is solved by application of the Pontryagin’s Maximum Principle, yielding an analytical expression for the optimal time-sampling in the SC. The second approach uses a discretization of the calculus of variations problem, resulting in a finite dimensional quadratic optimization problem. Solution of the latter provides a suboptimal time-sampling in the SC. The time-samplings,
obtained by these two approaches, are compared to each other in numerical examples.
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