Multivariate bounded process adjustment schemes

Nirmal Govind, Enrique del Castillo, George Runger, Mani Janakiram

Research output: Contribution to journalArticle

Abstract

We investigate multivariate process adjustment policies in the presence of fixed adjustment costs. A fixed adjustment cost leads to a trade-off between adjusting a process continuously and allowing the process to drift until a bound is violated. The problem of determining the best bounded adjustment policy and the optimal bounded adjustment parameter is addressed. Although the univariate bounded adjustment problem has received interest in the past, there has been little focus on the multivariate case in the literature. It has been shown that in the univariate case, the shape of the optimal adjustment policy is a deadband. Determining the shape of the optimal dead region and the parameter that defines this region in the multivariate case is a difficult problem. A State-Space model is formulated for the multivariate bounded process adjustment problem and a Kalman filter-based controller is used. With the help of simulation, the optimal bounded adjustment parameter is computed for two specific dead subspace shapes of practical applicability. An investigation of the performance of the simulation-optimization approach is included as the dimensionality of the observations increases. Validation of this approach with the only two analytic results available for deadbands (univariate and bivariate) confirms the accuracy of the optimal solutions found. An illustration in a semiconductor manufacturing process is presented and MATLAB code that implements the methods is developed and made available.

Original languageEnglish (US)
Pages (from-to)253-273
Number of pages21
JournalQuality Technology and Quantitative Management
Volume15
Issue number2
DOIs
StatePublished - Mar 4 2018

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Kalman filters
MATLAB
Costs
Semiconductor materials
Controllers
Adjustment process
Adjustment costs
Controller
Trade-offs
Dimensionality
Optimal solution
State-space model
Manufacturing process
Simulation
Simulation optimization
Kalman filter
Semiconductor manufacturing

All Science Journal Classification (ASJC) codes

  • Business and International Management
  • Industrial relations
  • Management Science and Operations Research
  • Information Systems and Management
  • Management of Technology and Innovation

Cite this

Govind, Nirmal ; del Castillo, Enrique ; Runger, George ; Janakiram, Mani. / Multivariate bounded process adjustment schemes. In: Quality Technology and Quantitative Management. 2018 ; Vol. 15, No. 2. pp. 253-273.
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Multivariate bounded process adjustment schemes. / Govind, Nirmal; del Castillo, Enrique; Runger, George; Janakiram, Mani.

In: Quality Technology and Quantitative Management, Vol. 15, No. 2, 04.03.2018, p. 253-273.

Research output: Contribution to journalArticle

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