Citation
Optimal schedule of a statistical process control with a nonlinear expected loss. In proceedings of the 7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015), 25 - 28 Aug 2015, Prague, Czech Republic, pages 42-54, 2015.
Paper
Abstract
A problem of constructing an optimal state-feedback schedule for a statistical process control with a variable sampling time-interval is considered. The aim of the schedule is to minimize the expected loss, caused by delay in detecting a process change. The case where this loss depends nonlinearly on the sampling time-interval is treated. Two approaches to the design of the optimal schedule are proposed. The ?rst approach based on converting the original optimization problem to an equivalent optimal control problem and applying to the latter the Pontryagin’s Maximum Principle, which leads to an exact analytical solution. The second approach is based on a discretization of the original problem and using proper mathematical programming tools to the discrete problem, which provides an approximate numerical solution. The schedules, obtained by these two approaches, are compared to each other in numerical examples. Moreover, in such examples, the analytical schedule is compared to the suboptimal composite schedule of a statistical process control, known in the literature
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Bibtex
@INPROCEEDINGS{2015-042-054-P, author = { V.Y. Glizer and V. Turetsky},
title = {Optimal schedule of a statistical process control with a nonlinear expected loss},
booktitle = {In proceedings of the 7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015), 25 - 28 Aug 2015, Prague, Czech Republic},
year = {2015},
editor = {Z. Hanzalek and G. Kendall and B. McCollum and P. Sucha},
pages = {42--54},
note = {Paper},
abstract = {A problem of constructing an optimal state-feedback schedule for a statistical process control with a variable sampling time-interval is considered. The aim of the schedule is to minimize the expected loss, caused by delay in detecting a process change. The case where this loss depends nonlinearly on the sampling time-interval is treated. Two approaches to the design of the optimal schedule are proposed. The ?rst approach based on converting the original optimization problem to an equivalent optimal control problem and applying to the latter the Pontryagin’s Maximum Principle, which leads to an exact analytical solution. The second approach is based on a discretization of the original problem and using proper mathematical programming tools to the discrete problem, which provides an approximate numerical solution. The schedules, obtained by these two approaches, are compared to each other in numerical examples. Moreover, in such examples, the analytical schedule is compared to the suboptimal composite schedule of a statistical process control, known in the literature},
owner = {Graham},
timestamp = {2017.01.16},
webpdf = {2015-042-054-P.pdf} }