# Sequential Design of Computer Experiments for Robust Parameter Design

Abstract (Summary)

Many physical systems can be modeled mathematically so that
“responses” are computable at arbitrary
“experimental” inputs using numerical methods
implemented by a complex computer code. In some cases, such
computer codes allow us to conduct analogs of physical experiments
that would not be possible due to the complexity of the required
physical system, cost of the physical experiment, or time
constraints. In a computer experiment, a response,
y(x)$, usually deterministic, is computed for each set of
input variables,
x, according to some experimental design strategy. Then, as
in physical experiments, the relationship between
x, the inputs, and
y(x)$, the outputs, is studied.
We are concerned with the design of computer experiments when
there are two types of inputs: control variables,
xc, and environmental variables,
xe. Control variables are set by a product designer
and environmental variables are those that are not controlled in
the field but have some probability distribution characterizing a
population of interest. Our interest is in the mean response
?(xc) = E[y(xc,
Xe)] as a function of the control variables, where
the expectation is taken over the distribution of the environmental
variables. The goal is to find a robust choice of control
variables. We review different methods of defining robustness and
focus on finding a set of control variables at which the response
is insensitive to the value of the environmental variables. Such a
choice ensures that the mean response is insensitive to
perturbations of the nominal environmental variable distribution.
We present a sequential strategy to select the inputs at which to
observe the response so as to determine a robust setting of the
control variables. Our solution is Bayesian; the prior takes the
response as a draw from a stationary Gaussian stochastic process.
The idea of the sequential algorithm is to compute the
“improvement” over the current optimal robust setting
for each untested site given the previous information; the design
selects the next site to maximize an expected improvement.
Bibliographical Information:

Advisor:

School:The Ohio State University

School Location:USA - Ohio

Source Type:Master's Thesis

Keywords:computer experiments control variables expected improvement noise sequential design

ISBN:

Date of Publication:01/01/2002