Estimation of mean and variance response surfaces in robust parameter design

Master'sMASTER OF ENGINEERIN

Robust Parameter Design With Computer Experiments Using Orthonormal Polynomials

<div><p>Robust parameter design with computer experiments is becoming increasingly important for product design. Existing methodologies for this problem are mostly for finding optimal control factor settings. However, in some cases, the objective of the experimenter may be to understand how the noise and control factors contribute to variation in the response. The functional analysis of variance (ANOVA) and variance decompositions of the response, in addition to the mean and variance models, help achieve this objective. Estimation of these quantities is not easy and few methods are able to quantity the estimation uncertainty. In this article, we show that the use of an orthonormal polynomial model of the simulator leads to simple formulas for functional ANOVA and variance decompositions, and the mean and variance models. We show that estimation uncertainty can be taken into account in a simple way by first fitting a Gaussian process model to experiment data and then approximating it with the orthonormal polynomial model. This leads to a joint normal distribution for the polynomial coefficients that quantifies estimation uncertainty. Supplementary materials for this article are available online.</p></div

Monotonic Metamodels for Deterministic Computer Experiments

<p>In deterministic computer experiments, it is often known that the output is a monotonic function of some of the inputs. In these cases, a monotonic metamodel will tend to give more accurate and interpretable predictions with less prediction uncertainty than a nonmonotonic metamodel. The widely used Gaussian process (GP) models are not monotonic. A recent article in <i>Biometrika</i> offers a modification that projects GP sample paths onto the cone of monotonic functions. However, their approach does not account for the fact that the GP model is more informative about the true function at locations near design points than at locations far away. Moreover, a grid-based method is used, which is memory intensive and gives predictions only at grid points. This article proposes the weighted projection approach that more effectively uses information in the GP model together with two computational implementations. The first is isotonic regression on a grid while the second is projection onto a cone of monotone splines, which alleviates problems faced by a grid-based approach. Simulations show that the monotone B-spline metamodel gives particularly good results. Supplementary materials for this article are available online.</p

Bayesian Optimal Designs for Efficient Estimation of the Optimum Point with Generalised Linear Models

10.1080/16843703.2018.1542965Quality Technology & Quantitative Management170189-10

Metamodel-based Optimization of Stochastic Computer Models for Engineering Design under Uncertain Objective Function

10.1080/24725854.2018.1504355IISE Transactions515517-53

Nonparametric Link Functions with Shape Constraints in Stochastic Degradation Processes: Application to Emerging Contaminants

10.1080/00224065.2019.1611353Journal of Quality Technology524370-38