Life Testing and Reliability Estimation

We develop a class of models for processes indexed in time and space that are based on autoregressive (AR) processes at each location. We use a Bayesian hierarchical structure to impose spatial coherence for the coefficients of the AR processes. The priors on such coefficients consist of spatial processes that guarantee time stationarity at each point in the spatial domain. The AR structures are coupled with a dynamic model for the mean of the process, which is expressed as a linear combination of time-varying parameters. We use satellite data on sea surface temperature for the North Pacific to illustrate how the model can be used to separate trends, cycles, and short-term variability for high-frequency environmental data. This article has supplementary material online.     

Extremes of multivariate ARMAX processes

We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained results, we derive new multivariate extreme value distributions. We characterize the extremal dependence by computing the multivariate extremal index and bivariate upper tail dependence coefficients. An estimation procedure for the multivariate extremal index is presented. We also address the marginal estimation and propose a new estimator for the ARMAX autoregressive parameter.     

A New Rank‐based Multivariate CUSUM Approach for Monitoring the Process Mean

In many cases, data do not follow a specific probability distribution in practice. As a result, a variety of distribution‐free control charts have been developed to monitor changes in the processes. An existing rank‐based multivariate cumulative sum (CUSUM) procedure based on the antirank vector does not quickly detect the large shift levels of the process mean. In this paper, we explore and develop an improved version of the existing rank‐based multivariate CUSUM procedure in order to overcome the difficulty. The numerical experiments show that the proposed approach dramatically outperforms the existing rank‐based multivariate CUSUM procedure in terms of the out‐of‐control average run length. In addition, the proposed approach particularly resolves the critical problem of the original approach, which occurs in the simultaneous shifts whose components are all the same but not 0. We believe that the proposed approach can be utilized for monitoring real data. Copyright © 2015 John Wiley & Sons, Ltd.     

Reconstruction of time-dependent boundary heat flux by a BEM-based inverse algorithm

The objective of this study is to reconstruct an unknown time-dependent heat flux distribution at a surface whose temperature history is provided by a broad-band thermochromic liquid crystal (TLC) thermographic technique. The information given for this inverse problem is the surface temperature history. Although this is not an inverse problem, it is solved as such in order to filter the errors in input temperatures which are reflected in errors in heat fluxes. We minimize a quadratic functional which measures the sum of the squares of the deviation of estimated (computed) temperatures relative to measured temperatures provided by the TLC thermography. The objective function is minimized using the Levenberg–Marquardt method, and we develop an explicit scheme to compute the required sensitivity coefficients. The unknown flux is allowed to vary in space and time. Results are presented for a simulation in which a spatially varying and time-dependent flux is reconstructed over an airfoil.     

Migration and dip-moveout seismic processes expressed as an invariant two-dimensional convolution

Migration and dip-moveout (partial prestack migration) are two-dimensional (space and time) processes of fundamental importance in digital processing of seismic data. Their goal is to make the seismic section appear similar to the geological image along the seismic line subsurface. In this article we study migration and dip-movement processes from the point of view of their impulse responses. The constant-velocity migration process is a space-invariant and time-variant operator. We demonstrate and illustrate by examples of synthetic and real seismic sections that by transforming the time axis with a square function the constant-velocity migration operator becomes temporally stationary as well as spatially stationary, that is, it can be expressed as an invariant two-dimensional convolution. The dip-moveout seismic process can be applied to constant-offset seismic sections or to shot seismic profiles. The application of dip-moveout process to constant-offset sections is also a temporally varying and spatially stationary operator. By transforming the time axis with a logarithmic function the constant-offset dip-moveout operator becomes temporally stationary as well as spatially stationary. The shot dip-moveout operator is space variant and time variant. After a logarithmic transformation of both the time and the space coordinates, it becomes time invariant and space invariant. Therefore the dip-moveout seismic processes can be also expressed as an invariant two-dimensional convolution. We illustrate this by examples of synthetic seismic sections.     

Shape testing in varying coefficient models

We consider varying coefficient models which are an extension of the classical linear regression models in the sense that the regression coefficients are replaced by functions in certain variables (often time). Varying coefficient models have been popular in longitudinal data and panel data studies, and have been applied in fields, such as finance and health sciences. We estimate the coefficient functions by splines. An important question in a varying coefficient model is whether a coefficient function is monotone or convex. We develop consistent testing procedures for monotonicity and convexity. Moreover, we provide procedures to test simultaneously the shapes of certain coefficient functions in a varying coefficient model. The tests use constrained and unconstrained regression splines. The performances of the proposed tests are illustrated on simulated data. We also give a real data application.     

Large-Vector Autoregression for Multilayer Spatially Correlated Time Series

One of the most commonly used methods for modeling multivariate time series is the vector autoregressive model (VAR). VAR is generally used to identify lead, lag, and contemporaneous relationships describing Granger causality within and between time series. In this article, we investigate the VAR methodology for analyzing data consisting of multilayer time series that are spatially interdependent. When modeling VAR relationships for such data, the dependence between time series is both a curse and a blessing. The former because it requires modeling the between time-series correlation or the contemporaneous relationships which may be challenging when using likelihood-based methods. The latter because the spatial correlation structure can be used to specify the lead–lag relationships within and between time series, within and between layers. To address these challenges, we propose an L₁\L₂ regularized likelihood estimation method. The lead, lag, and contemporaneous relationships are estimated using an efficient algorithm that exploits sparsity in the VAR structure, accounts for the spatial dependence, and models the error dependence. We consider a case study to illustrate the applicability of our method. In the supplementary materials available online, we assess the performance of the proposed VAR model and compare it with existing methods within a simulation study.     

Nonstationary multivariate process modeling through spatially varying coregionalization

Models for the analysis of multivariate spatial data are receiving increased attention these days. In many applications it will be preferable to work with multivariate spatial processes to specify such models. A critical specification in providing these models is the cross covariance function. Constructive approaches for developing valid cross-covariance functions offer the most practical strategy for doing this. These approaches include separability, kernel convolution or moving average methods, and convolution of covariance functions. We review these approaches but take as our main focus the computationally manageable class referred to as the linear model of coregionalization (LMC). We introduce a fully Bayesian development of the LMC. We offer clarification of the connection between joint and conditional approaches to fitting such models including prior specifications. However, to substantially enhance the usefulness of such modelling we propose the notion of a spatially varying LMC (SVLMC) providing a very rich class of multivariate nonstationary processes with simple interpretation. We illustrate the use of our proposed SVLMC with application to more than 600 commercial property transactions in three quite different real estate markets, Chicago, Dallas and San Diego. Bivariate nonstationary process inodels are developed for income from and selling price of the property. The work of the first and second authors was supported in part by NIH grant R01ES07750-06.     

A discrete spatial model for wafer yield prediction

Yield analysis is one of the key concerns in the fabrication of semiconductor wafers. An effective yield analysis model will contribute to production planning and control, cost reductions and the enhanced competitiveness of enterprises. In this article, we propose a novel discrete spatial model based on defect data on wafer maps for analyzing and predicting wafer yields at different chip locations. More specifically, based on a Bayesian framework, we propose a hierarchical generalized linear mixed model, which incorporates both global trends and spatially correlated effects to characterize wafer yields with clustered defects. Both real and simulated data are used to validate the performance of the proposed model. The experimental results show that the newly proposed model offers an improved fit to spatially correlated wafer map data.     

Bridging semantic gap between high-level and low-level features in content-based video retrieval using multi-stage ESN–SVM classifier

Content-based video retrieval system aims at assisting a user to retrieve targeted video sequence in a large database. Most of the search engines use textual annotations to retrieve videos. These types of engines offer a low-level abstraction while the user seeks high-level semantics. Bridging this type of semantic gap in video retrieval remains an important challenge. In this paper, colour, texture and shapes are considered to be low-level features and motion is a high-level feature. Colour histograms convert the RGB colour space into YcbCr and extract hue and saturation values from frames. After colour extraction, filter mask is applied and gradient value is computed. Gradient and threshold values are compared to draw the edge map. Edges are smoothed for sharpening to remove the unnecessary connected components. These diverse shapes are then extracted and stored in shape feature vectors. Finally, an SVM classifier is used for classification of low-level features. For high-level features, depth images are extracted for motion feature identification and classification is done via echo state neural networks (ESN). ESN are a supervised learning technique and follow the principle of recurrent neural networks. ESN are well known for time series classification and also proved their effective performance in gesture detection. By combining the existing algorithms, a high-performance multimedia event detection system is constructed. The effectiveness and efficiency of proposed event detection mechanism is validated using MSR 3D action pair dataset. Experimental results show that the detection accuracy of proposed combination is better than those of other algorithms     

A unified statistical framework for monitoring multivariate systems with unknown source and error signals

This article proposes a unified multivariate statistical monitoring framework that incorporates recent work on maximum likelihood PCA (MLPCA) into conventional PCA-based monitoring. The proposed approach allows the simultaneous and consistent estimation of the PCA model plane, its dimension and the error covariance matrix. This paper also invokes recent work on monitoring non-Gaussian processes to extract unknown Gaussian as well as non-Gaussian source signals from recorded process data. By contrasting the unified framework with PCA-based process monitoring using a simulation example and recorded data from two industrial processes, the proposed approach produced more accurate and/or sensitive monitoring models.     

A new bivariate integer-valued GARCH model allowing for negative cross-correlation

Univariate integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, have been well studied in the literature, but there is little progress in multivariate models. Although some multivariate INAR models were proposed, they do not provide enough flexibility in modeling count data, such as volatility of numbers of stock transactions. Then, a bivariate Poisson INGARCH model was suggested by Liu (Some models for time series of counts, Dissertations, Columbia University, 2012), but it can only deal with positive cross-correlation between two components. To remedy this defect, we propose a new bivariate Poisson INGARCH model, which is more flexible and allows for positive or negative cross-correlation. Stationarity and ergodicity of the new process are established. The maximum likelihood method is used to estimate the unknown parameters, and consistency and asymptotic normality for estimators are given. A simulation study is given to evaluate the estimators for parameters of interest. Real and artificial data examples are illustrated to demonstrate good performances of the proposed model relative to the existing model.     

Informative Sensor and Feature Selection via Hierarchical Nonnegative Garrote

Placing sensors in every station of a process or every element of a system to monistor its state or performance is usually too expensive or physically impossible. Therefore, a systematic method is needed to select important sensing variables. The method should not only be capable of identifying important sensors/signals among multistream signals from a distributed sensing system, but should also be able to extract a small set of interpretable features from the high-dimensional vector of a selected signal. For this purpose, we develop a new hierarchical regularization approach called hierarchical nonnegative garrote (NNG). At the first level of hierarchy, a group NNG is used to select important signals, and at the second level, the individual features within each signal are selected using a modified version of NNG that possesses good properties for the estimated coefficients. Performance of the proposed method is evaluated and compared with other existing methods through Monte Carlo simulation. A case study is conducted to demonstrate the proposed methodology that can be applied to develop a predictive model for the assessment of vehicle design comfort based on the tested drivers’ motion trajectory signals. This article has supplementary material online.     

An Introduction to Generalized Linear Models

Particle size is commonly used to determine quality and predict performance of particle systems. We consider particle size distributions inferred from a material sample using a fixed number of sieves with progressively smaller size openings, where the weight of the particles in each size interval is measured. In this article, we propose Bayes analyses for data from particle sieving studies based on parsimoniously parameterized multivariate normal approximate models for vectors of log weight fraction ratios. Additionally, we observe that the basic approach extends directly to modeling mixture contexts, which provides model flexibility and is a very natural extension when physical mixtures of materials with fundamentally different particle sizes are encountered. We also consider hierarchical modeling, where a single process produces lots of particles and the data available are (replicated) weight fraction vectors from different lots. Supplementary materials for this article are available online.     

Bootstrapping forecast intervals in ARCH models

In this paper we develop a bootstrap method for the construction of prediction intervals for an ARMA model when its innovations are an autoregressive conditional heteroscedastic process. We give a proof of the validity of the proposed bootstrap for this process. For this purpose we prove the convergence to zero in probability of the Mallows metric between the empirical distribution function and the theoretical distribution function of the residuals. The potential of the proposed method is assessed through a simulation study. This research was partially supported by Grant UZ-228-26 from the Spanish Ministry of Education and Grant UZ-228-25 from University of Zaragoza.     

Detecting the process changes for multivariate nonlinear profile data

In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out‐of‐control average run length (ARL₁ ). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes.     

A kind of multilevel authentication system for multiple-image by modulated real part synthesis and iterative phase multiplexing

A kind of multilevel authentication system for multiple-image based on modulated real part synthesis and iterative phase multiplexing in the Fresnel domain is proposed. In the design process of the low-level authentication system, a series of normalized real part information are iteratively generated by phase retrieval algorithm in the Fresnel domain, and the final private keys for different individual low-level certification images can be fabricated by binary amplitude modulation, superposition, synthesis, and sampling; while in the design process of the high-level authentication system, the final private keys for different individual high-level certification images can be generated by iterative phase information encoding and multiplexing. During the high-level authentication, the meaningful certification image can be reconstructed by the inverse Fresnel transform with the corresponding correct private keys, meanwhile, the correlation coefficient is utilized as judgment criterion; while in the low-level authentication, with the help of correct keys, the noise-like image with meaningless information can be recovered, but a remarkable peak output in the nonlinear correlation coefficient can be generated, which is adopted as the criterion to judge whether the low-level authentication is successful or not. Theoretical analysis and numerical simulations both verify the feasibility of the proposed method.     

Analyzing market baskets by restricted Boltzmann machines

We introduce a model which differs from the well-known multivariate logit model (MVL) used to analyze the cross-category dependence in market baskets by the addition of binary hidden variables. This model is called restricted Boltzmann machine (RBM) and new to the marketing literature. Extant applications of the MVL model for higher numbers of categories typically follow a two-step approach as simultaneous maximum likelihood estimation is computationally infeasible. In contrast to the MVL, the RBM can be simultaneously estimated by maximum likelihood even for a higher number of categories as long as the number of hidden variables is moderate. We measure the cross-category dependence by pairwise marginal cross effects which are obtained using estimated coefficients and sampling of baskets. In the empirical study, we analyze market baskets consisting of the 60 most frequently purchased categories of the assortment of a supermarket. For a validation data set, the RBM performs better than the MVL model estimated by maximum pseudo-likelihood. For our data, about 75 % of the baskets are reproduced by the model without cross-category dependence, but 25 % of the baskets cannot be adequately modeled if cross effects are ignored. Moreover, it turns out that both the number of significant cross effects and their relationships can be grasped rather easily.     

A variable parameters multivariate control chart for simultaneous monitoring of the process mean and variability with measurement errors

Evaluating the effect of measurement errors on either adaptive or simultaneous control charts has been a topic of interest for the researchers in the recent years. Nevertheless, the effect of measurement errors on both adaptive and simultaneous monitoring control charts has not been considered yet. In this paper, through extensive numerical studies, we evaluate the effect of measurement errors on an adaptive (variable parameters) simultaneous multivariate control chart for the mean vector and the variance-covariance matrix of p quality characteristics assumed to follow a multivariate normal distribution. In order to do so, (a) we use eight performance measures computed using a Markov chain model, (b) we consider the effects of multiple measurements as well as the error model's parameters, and (c) we also consider the overall performance of this adaptive simultaneous chart including the chart parameters values optimization, which have never been considered so far for this scheme. At last, a real case is presented in order to illustrate the proposed scheme.