Optimal Time-sampling Problem in a Statistical Control with a Quadratic Cost Functional - Analytical and Numerical Approaches

Valery Y. Glizer, Vladimir Turetsky

2018

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.

Paper Citation

in Harvard Style

Y. Glizer V. and Turetsky V. (2018). Optimal Time-sampling Problem in a Statistical Control with a Quadratic Cost Functional - Analytical and Numerical Approaches.In Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-321-6, pages 21-32. DOI: 10.5220/0006829000210032

in Bibtex Style

@conference{icinco18,
author={Valery Y. Glizer and Vladimir Turetsky},
title={Optimal Time-sampling Problem in a Statistical Control with a Quadratic Cost Functional - Analytical and Numerical Approaches},
booktitle={Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2018},
pages={21-32},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006829000210032},
isbn={978-989-758-321-6},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Optimal Time-sampling Problem in a Statistical Control with a Quadratic Cost Functional - Analytical and Numerical Approaches
SN - 978-989-758-321-6
AU - Y. Glizer V.
AU - Turetsky V.
PY - 2018
SP - 21
EP - 32
DO - 10.5220/0006829000210032