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The study focuses on reducing noise and nonstationary backgrounds in data collected through active infrared thermography (AIRT) for defect detection in materials. The authors employ adaptive fixed-rank kriging to analyze a sequence of thermograms obtained in the AIRT experiment. Using basis functions derived from thin-plate splines, the data features are represented at various resolution levels, resulting in a concise spatial covariance function representation. Eigenfunctions are then derived from the estimated covariance function to capture spatial structures at different scales. Visualizing these eigenfunctions highlights defect information. The authors validate their approach through a pulsed thermography experiment on a carbon-fiber-reinforced plastic (CFRP) sample, demonstrating its effectiveness in detecting defects. [ABSTRACT FROM AUTHOR]

Factor models have been widely used in recent years to model high‐dimensional spatio‐temporal data. However, the validity of employing factor models in a specific application has received less attention. This article proposes test statistics for testing the symmetry in cross‐correlation matrices of a high‐dimensional stochastic process implied by exact factor models. A rejection of symmetry indicates that the use of an exact factor model is questionable. Both simulations and real examples are used to demonstrate the applications and to study the finite‐sample performance of the proposed test statistics. Empirical results show that the proposed test statistics are effective in identifying cases where exact factor models are not appropriate, providing valuable guidance for choosing factor models in a high‐dimensional setting. [ABSTRACT FROM AUTHOR]

The double exponentially weighted moving average (dEWMA) feedback control scheme, a conventional run-to-run control scheme, can adjust certain semiconductor manufacturing processes with a linear drift. The long-term stability conditions for this closed-loop system have received considerable attention in literature. These stability conditions can be expressed in terms of the predicted model assuming that an initial process input-output (I-O) predicted model can be obtained successfully in advance. However, the predicted model is constructed by a random sample of I-O variables, and therefore the strength of the linear relationship between I-O variables plays a major role in determining the validation of these stability conditions. In order to design a stable dEWMA control scheme, the covariance (or correlation) structure of I-O variables and the number of experiments should be simultaneously considered. By controlling a guaranteed probability of stability, this study first derives the formula for an adequate sample size required to construct the predicted model in the case of single-input single-output and multiple-input single-output systems. Illustrative examples demonstrate the effectiveness of the covariance structure of I-O variables in determining the sample size. Implications for research on multiple-input multiple-output systems are also addressed. Index Terms--Double exponentially weighted moving average (dEWMA) control scheme, multiple correlation coefficient, run-to-run process control, sample size, stability conditions.

The spatial subsampling method is an ideal approach for predicting the spatial cumulative distribution function. This approach makes use of nonparametric subsampling and thus considers the adequacy of available data to provide an accurate representation of the underlying spatial process, in contrast with parametric modeling which assumes that the fundamental property of the spatial process has been adequately captured in the assigned model. In this regard, the need for a complete grid of data in spatial subsampling is justified., We thank all discussants for their penetrating comments and for the time they have devoted to this project. The diverse set of comments, suggestions, and alternative approaches put forward in [...]

In existing pH acceleration models, which are used to assess the shelf-life of liquid-phase nano-sol products, a mixture of normal distributions is commonly employed to describe the sizes of particles mixing from two populations. The Gaussian mixture model approach falls short when used to characterize the asymmetric distributions of particle sizes in subgroups. This work considers instead a broader class of a mixture of log-F distributions, to be embedded in a pH acceleration model. This study aims at understanding the impact of the new modeling approach, in the presence of model misspecification of the particle size distribution, on the accuracy and precision for making the shelf-life predictions. This study found that model misspecification indeed significantly affects the shelf-life predictions. The proposed method shows favorable finite sample performance on a simulated data set. Both the quantitative analysis of the impact due to model misspecification and the solution proposed herein could benefit practitioners in the long run. [ABSTRACT FROM AUTHOR]

We develop a new approach for modeling non-stationary spatial-temporal processes on the basis of data sampled at fixed locations over time. The approach applies a basis function formulation and a constrained penalized least squares method recently proposed for estimating non-stationary spatial-only covariance functions. In this article, we further incorporate the temporal dependence into this framework and model the spatial-temporal process as the sum of a spatial-temporal stationary process and a linear combination of known basis functions with temporal dependent coefficients. A group lasso penalty is devised to select the basis functions and estimate the parameters simultaneously. In addition, a blockwise coordinate descent algorithm is applied for implementation. This algorithm computes the constrained penalized least squares solutions along a regularization path very rapidly. The resulting dynamic model has a state-space form, thereby the optimal spatial-temporal predictions can be computed efficiently using the Kalman filter. Moreover, the methodology is applied to a wind speed data set observed at the western Pacific Ocean for illustration. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]