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In the general setting of long‐memory multivariate time series, the long‐memory characteristics are defined by two components. The long‐memory parameters describe the autocorrelation of each time series. And the long‐run covariance measures the coupling between time series, with general phase parameters. It is of interest to estimate the long‐memory, long‐run covariance and general phase parameters of time series generated by this wide class of models although they are not necessarily Gaussian nor stationary. This estimation is thus not directly possible using real wavelets decomposition or Fourier analysis. Our purpose is to define an inference approach based on a representation using quasi‐analytic wavelets. We first show that the covariance of the wavelet coefficients provides an adequate estimator of the covariance structure including the phase term. Consistent estimators based on a local Whittle approximation are then proposed. Simulations highlight a satisfactory behavior of the estimation on finite samples on multivariate fractional Brownian motions. An application on a real neuroscience dataset is presented, where long‐memory and brain connectivity are inferred. [ABSTRACT FROM AUTHOR]

In the context of big data, multivariate processes must often be monitored in a timely and accurate manner. Usually, the distribution of process variables is unknown. This paper proposes a new strategy for multivariate process monitoring when the distribution of a process variable is unknown. We address monitoring by means of a rank-based method that is completely nonparametric. We also discuss the optimal strategy of parameters. A simulation study demonstrates that the proposed method is efficient in detecting shifts for multivariate processes. A real data example is presented to illustrate the performance of the proposed method. [ABSTRACT FROM AUTHOR]

This paper describes the methodology used by the team RedSea in the data competition organized for EVA 2021 conference. We develop a novel two-part model to jointly describe the wildfire count data and burnt area data provided by the competition organizers with covariates. Our proposed methodology relies on the integrated nested Laplace approximation combined with the stochastic partial differential equation (INLA-SPDE) approach. In the first part, a binary non-stationary spatio-temporal model is used to describe the underlying process that determines whether or not there is wildfire at a specific time and location. In the second part, we consider a non-stationary hurdle log-Gaussian Cox process (hurdle-LGCP) for the positive wildfire count data, i.e., an LGCP is used to model the shifted positive count data, and a non-stationary log-Gaussian model for positive burnt area data. Dependence between the positive count data and positive burnt area data is captured by a shared spatio-temporal random effect. Our two-part modeling approach performs well in terms of the prediction score criterion chosen by the data competition organizers. Moreover, our model results show that surface pressure is the most influential driver for the occurrence of a wildfire, whilst surface net solar radiation and surface pressure are the key drivers for large numbers of wildfires, and temperature and evaporation are the key drivers of large burnt areas. [ABSTRACT FROM AUTHOR]

The segmentation of data into stationary stretches, also known as the multiple change point problem, is important for many applications in time series analysis and signal processing. Based on strong invariance principles, we analyze a data segmentation methodology using moving sum statistics for a class of regime-switching multivariate processes, where each switch results in a change in the drift. In particular, this framework includes the data segmentation of multivariate partial sum, integrated diffusion, and renewal processes, even if the distance between the change points is sublinear. We study the asymptotic behavior of the corresponding change point estimators, show their consistency, and derive the corresponding localization rates, which are minimax optimal in a variety of situations, including an unbounded number of changes in Wiener processes with drift. Furthermore, we derive the limit distribution of the change point estimators for local changes. This result can, in principle, be used to derive confidence intervals for the change points. [ABSTRACT FROM AUTHOR]

This paper proposes a two-step method for monitoring high-dimensional normally distributed multi-stream processes. The first step consists of a single Hotelling chi-square chart, while the second includes a Shewhart chart for each stream to diagnose off-target streams. The second step is needed only if an alarm triggered in the first step. The required control limits and performance measures such as statistical power and ARLs are computed exactly and efficiently for both cases of independent and dependent streams. The new method performs well in detecting small shifts and has a competitive statistical performance relative to a recent method. [ABSTRACT FROM AUTHOR]

Alarm monitoring, which is implemented by an alarm system, is to generate alarms for a process through certain mechanisms when the process is in the abnormal condition. This brief proposes a method to design an alarm system with dynamic alarm limits for multivariate processes. A normal operating zone (NOZ) described by a convex hull is established from the historical normal data points based on a formulated fitness index, and dynamic alarm limits of each process variable are developed based on the established NOZ. If all process variables are inside their own dynamic alarm limits, the process is in the normal condition and no alarms are raised; otherwise, the process is in the abnormal condition and alarms will occur. The designed alarm system can avoid false alarms from the conventional one using static alarm limits, owing to a fact that dynamic alarm limits of one process variable are related to other process variables. In addition, unlike designing alarm limits for latent variables with no specific meanings, each process variable has its own dynamic alarm limits that have the same physical meaning as the process variable. Industrial examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

We propose to control the mean vector by taking larger samples but inspecting fewer quality characteristics if we work with samples of size n to control bivariate processes, then 2n observations are usually collected, half are observations of X1 and the other half are observations of X2; alternatively, we might work with samples of size 2n if only observations of X1 (or X2) are collected; in both cases the cardinality c of the sample data set is c = 2n. If only one of the two quality characteristics, X1 or X2, is measured at each sampling time, then only one of the two statistics ( X ¯ 1 or X ¯ 2 ) is computed. The variable charting statistic (VCS) chart works as follows: if a X ¯ 1 point falls in the central region, then the statistic for the next sample changes to X ¯ 2 and vice-versa; yet, if a X ¯ 1 point reaches the warning region, then the statistic for the next sample remains X ¯ 1 . [ABSTRACT FROM AUTHOR]

To monitor the quality of a multi-attribute process, some issues arise. One of them being the occurrence of a high number of false alarms (type I error) and the other an increase in the probability of not detecting defects when the process is monitored by a set of independent uni-attribute control charts. In this paper, based upon the artificial neural network capabilities we develop a new methodology to overcome this problem. We design a perceptron neural network to monitor either the proportions of several types of product nonconformities (instead of using several np charts) or the number of different types of defects (instead of using several c charts) in a product. Moreover, while the proposed method possesses the ability to be applied for small sample sizes, it is also able to diagnose the mean shift online. We present two simulation experiments in which the proportions of several types of nonconformities are monitored. In addition, we present one more simulation experiment in which the number of different types of defect is controlled. We also compare the performance of the proposed methodology with the ones from the Mnp and T2 charts for multi-attribute processes. The results of the simulation studies are encouraging. [ABSTRACT FROM AUTHOR]

Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real-data applications, the correlation between time series is crucial. Usual estimations of correlation can be highly biased owing to phase shifts caused by the differences in the properties of autocorrelation in the processes. To address this issue, we introduce a semiparametric estimation of multivariate long-range dependent processes. The parameters of interest in the model are the vector of the long-range dependence parameters and the long-run covariance matrix, also called functional connectivity in neuroscience. This matrix characterizes coupling between time series. The proposed multivariate wavelet-based Whittle estimation is shown to be consistent for the estimation of both the long-range dependence and the covariance matrix and to encompass both stationary and nonstationary processes. A simulation study and a real-data example are presented to illustrate the finite-sample behaviour. [ABSTRACT FROM AUTHOR]

In this study, a new statistical monitoring technique based on efficient projection to latent structures (EPLS) is proposed for quality‐relevant fault detection in multivariate processes that exhibit collinear measurements. The algorithm decomposes process variables into three subspaces according to singular value decomposition (SVD) and principal component analysis. This method effectively solves the problems of real‐time and effectiveness in the quality‐relevant fault diagnosis of industrial processes. EPLS takes full advantage of good nature of SVD. As a result, the calculation of the projection process is greatly reduced. It is reasonable that the process data space was projected to three subspaces, a quality‐relevant subspace, a quality‐irrelevant subspace and a residual subspace. EPLS algorithm not only effectively avoids the tedious iterative calculation, but also makes more explicit spatial resolution. The framework of quality‐relevant fault monitoring based on EPLS algorithm was proposed as well in this study. A challenging problem, real industrial hot strip mill process, is used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The use of principal component analysis in measuring the capability of a multivariate process is an issue initially considered by Wang and Chen (1998). In this article, we extend their initial idea by proposing new indices that can be used in situations where the specification limits of the multivariate process are unilateral. Moreover, some new indices for multivariate processes are suggested. These indices have been developed so as to take into account the proportion of variance explained by each principal component, thus making the measurement of process capability more effective. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Spectral measures of causality are used to explore the role of different rhythms in the causal connectivity between brain regions. We study several spectral measures related to Granger causality, comprising the bivariate and conditional Geweke measures, the directed transfer function, and the partial directed coherence. We derive the formulation of dependence and causality in the spectral domain from the more general formulation in the information-theory framework. We argue that the transfer entropy, the most general measure derived from the concept of Granger causality, lacks a spectral representation in terms of only the processes associated with the recorded signals. For all the spectral measures we show how they are related to mutual information rates when explicitly considering the parametric autoregressive representation of the processes. In this way we express the conditional Geweke spectral measure in terms of a multiple coherence involving innovation variables inherent to the autoregressive representation. We also link partial directed coherence with Sims' criterion of causality. Given our results, we discuss the causal interpretation of the spectral measures related to Granger causality and stress the necessity to explicitly consider their specific formulation based on modeling the signals as linear Gaussian stationary autoregressive processes. [ABSTRACT FROM AUTHOR]

For the univariate case, the R chart and the S2 chart are the most common charts used for monitoring the process dispersion. With the usual sample size of 4 and 5, the R chart is slightly inferior to the S2 chart in terms of efficiency in detecting process shifts. In this article, we show that for the multivariate case, the chart based on the standardized sample ranges, we call the RMAX chart, is substantially inferior in terms of efficiency in detecting shifts in the covariance matrix than the VMAX chart, which is based on the standardized sample variances. The user's familiarity with sample ranges is a point in favor of the RMAX chart. An example is presented to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

The capability analysis of production processes where there are more than one correlated quality variables is a complicated task. The problem becomes even more difficult when these variables exhibit nonnormal characteristics. In this paper, a new methodology is proposed to estimate process capability indices (PCIs) of multivariate nonnormal processes. In the proposed methodology, the skewness of the marginal probability distributions of the variables is first diminished by a root transformation technique. Then, a Monte Carlo simulation method is employed to estimate the process proportion of nonconformities (PNC). Next, the relationship between PNC and PCI is found, and finally, PCI is estimated using PNC. Several multivariate nonnormal distributions such as Beta, Weibull, and Gamma are taken into account in simulation experiments. A real-world problem is also given to demonstrate the application of the proposed procedure. The results obtained from both the simulation studies and the real-world problem show that the proposed method performs well and is able to estimate PCI properly. [ABSTRACT FROM AUTHOR]

The main usefulness of a capability index is to relate the actual variability of the process with the admissible one. This admissible variability is, in turn, related with the nonconforming proportion. Hence, the capability index should be closely related to the nonconforming proportion. In univariate and centered processes, the classical C p index explicitly admits this interpretation. For instance, if C p = 0.5, the standard deviation should be reduced to 50% to attain C p = 1. However, for noncentered processes and multivariate processes, there is a lack of capability indices that admit such an interpretation. This article fills this gap in the literature and proposes univariate and multivariate capability indices that have a direct interpretation of how much the variability of the process should increase or decrease to attain a unitary index. Some numerical examples are used to compare the proposed indices with the existing ones, showing the advantages of the proposals. [ABSTRACT FROM AUTHOR]

In this article, we propose a control chart for detecting shifts in the covariance matrix of a multivariate process. The monitoring statistic is based on the standardized sample variance of p quality characteristics we call the VMAX statistic. The points plotted on the chart correspond to the maximum of the values of these p variances. The reasons to consider the VMAX statistic instead of the generalized variance | S| are faster detection of process changes and better diagnostic features, which mean that the VMAX statistic is better at identifying the out-of-control variable. User’s familiarity with sample variances is another point in favor of the VMAX statistic. An example is presented to illustrate the application of the proposed chart. [ABSTRACT FROM AUTHOR]

This paper describes a methodology for the simulation of out-of-control situations using in-control data, for the purpose of identifying the potential alarms that could occur in a multivariate process. The method is based on finding the independent factors of the variability of the process and shifting these factors one by one. The effects of these shifts are then translated in terms of the observed variables. The shifts provoked by the most important factors are called principal alarms. The principal alarms can be plotted, visualizing the main deviations of the process. Also, a resampling procedure for the estimation of the average run length of a control chart using principal alarms is proposed. An application with a real industrial process illustrates the usefulness of the methodology. [ABSTRACT FROM AUTHOR]

A general framework for the construction of control charts is presented. The method is based on using the density of the sample subgroup statistic as a measure of how unusual newly observed subgroups are. This methodology includes, as special cases, many common control chart techniques. The method is also easily applied to multivariate and multimodal situations. A non-parametric control chart is implemented by estimating the density of the sample subgroup statistic using a kernel estimator of the bootstrap distribution of the observed subgroup statistics. Several examples of the method are presented in the parametric and non-parametric situations. The potential performance of the non-parametric version of the method is demonstrated through an empirical study of average run length properties. Copyright © 2005 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]