Response Surface Optimization in the Presence of Internal Noise With Application to Optimal Alignment of Carbon Nanotubes

TY - JOUR

T1 - Response Surface Optimization in the Presence of Internal Noise With Application to Optimal Alignment of Carbon Nanotubes

AU - Sosina, Sobambo

AU - Remillard, E. Marielle

AU - Zhang, Qiaoying

AU - Vecitis, Chad

AU - Dasgupta, Tirthankar

N1 - Publisher Copyright: © 2018, © 2018 American Statistical Association and the American Society for Quality.

PY - 2019/1/2

Y1 - 2019/1/2

N2 - Internal noise, which means fluctuation of input factors around their set values, is common in many experiments in the physical and engineering sciences. Existing methods for response surface optimization in the presence of internal noise typically adopt a two-step approach: (a) fitting a response model as a function of the set value and (b) using Monte Carlo methods to account for internal noise while optimizing the response. In this article, motivated by a problem in optimizing alignment of carbon nanotubes (CNT), we propose a Bayesian approach for response surface optimization in the presence of internal noise. A unit-free and interpretable measure to quantify the strength of internal noise is proposed. Suitable objective functions or performance measures consistent with the overall goal of optimizing the response function are identified, methods for estimating them from available experimental data are suggested, and simulations are conducted to compare them with respect to their ability to account for internal noise in the optimization problem. The loss accrued by ignoring the internal noise in the optimization problem is quantified and studied via simulation. The proposed method is demonstrated through its application in the CNT alignment problem.

AB - Internal noise, which means fluctuation of input factors around their set values, is common in many experiments in the physical and engineering sciences. Existing methods for response surface optimization in the presence of internal noise typically adopt a two-step approach: (a) fitting a response model as a function of the set value and (b) using Monte Carlo methods to account for internal noise while optimizing the response. In this article, motivated by a problem in optimizing alignment of carbon nanotubes (CNT), we propose a Bayesian approach for response surface optimization in the presence of internal noise. A unit-free and interpretable measure to quantify the strength of internal noise is proposed. Suitable objective functions or performance measures consistent with the overall goal of optimizing the response function are identified, methods for estimating them from available experimental data are suggested, and simulations are conducted to compare them with respect to their ability to account for internal noise in the optimization problem. The loss accrued by ignoring the internal noise in the optimization problem is quantified and studied via simulation. The proposed method is demonstrated through its application in the CNT alignment problem.

KW - Bayesian approach

KW - Internal noise

KW - Nanostructures

KW - Robust parameter design

UR - http://www.scopus.com/inward/record.url?scp=85056101531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85056101531&partnerID=8YFLogxK

U2 - 10.1080/00401706.2018.1442750

DO - 10.1080/00401706.2018.1442750

M3 - Article

SN - 0040-1706

VL - 61

SP - 50

EP - 65

JO - Technometrics

JF - Technometrics

IS - 1

ER -