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The current monitoring of modern distribution networks by operators with the aim to improve the network visibility and thus detect and mitigate challenges such as power quality issues has resulted in massive data generation. Such data need to be analysed and technical observations realised. Thus, this paper presents bad data detection for spatiotemporal harmonic power quality field measurements obtained from six power quality analysers (installed at the connection points of customer-owned photovoltaic and small-scale energy storage and the mains units) with high level of granularity (1s interval). A total of 4.1 billion measured values have been evaluated in the bad data detection. Multivariate statistical methods (principal component analysis and Hotelling’s T2 statistic) have been combined with Bag of Little Bootstrap (BLB) to analyse the massive data. Specifically, the BLB technique has been deployed for calculating the upper control limit for the bad data detection, thus, the spatiotemporal nature of the data has been fully captured. The method has been applied to harmonic load flow analysis of a practical distribution network. The findings reveal how the neglect of spatiotemporality could conceal the actual harmonic penetration levels in a data-driven harmonic load flow analysis. Other interesting technical findings are presented.

In recent years various probability models have been proposed for describing lifetime data. Increasing model flexibility is often sought as a means to better describe asymmetric and heavy tail distributions. Such extensions were pioneered by the beta‐G family. However, efficient (GoF) measures for the beta‐G distributions are sought. In this paper, we combine probability weighted moments (PWMs) and the Mellin transform (MT) in order to furnish new qualitative and quantitative GoF tools for model selection within the beta‐G class. We derive PWMs for the Fréchet and Kumaraswamy distributions, and we provide expressions for the MT, and for the log‐cumulants (LC) of the beta‐Weibull, beta‐Fréchet, beta‐Kumaraswamy, and beta‐log‐logistic distributions. Subsequently, we construct LC diagrams and, based on the Hotelling's T2 statistic, we derive confidence ellipses for the LCs. Finally, the proposed GoF measures are applied on five real data sets in order to demonstrate their applicability. [ABSTRACT FROM AUTHOR]

The current monitoring of modern distribution networks by operators with the aim to improve the network visibility and thus detect and mitigate challenges such as power quality issues has resulted in massive data generation. Such data need to be analysed and technical observations realised. Thus, this paper presents bad data detection for spatiotemporal harmonic power quality field measurements obtained from six power quality analysers (installed at the connection points of customer-owned photovoltaic and small-scale energy storage and the mains units) with high level of granularity (1s interval). A total of 4.1 billion measured values have been evaluated in the bad data detection. Multivariate statistical methods (principal component analysis and Hotelling's T 2 statistic) have been combined with Bag of Little Bootstrap (BLB) to analyse the massive data. Specifically, the BLB technique has been deployed for calculating the upper control limit for the bad data detection, thus, the spatiotemporal nature of the data has been fully captured. The method has been applied to harmonic load flow analysis of a practical distribution network. The findings reveal how the neglect of spatiotemporality could conceal the actual harmonic penetration levels in a data-driven harmonic load flow analysis. Other interesting technical findings are presented. • Calculate UCL for bad data detection of practical spatiotemporal PQ massive data. • Apply proposed bad data detection to harmonic load flow of a distribution network • Visualise harmonic evolution during PV, SSES and consumer load operations. • Apply multivariate statistical control approach to harmonic PQ massive data analytics. [ABSTRACT FROM AUTHOR]

An extension of the D2 test statistic to test the equality of mean for high-dimensional and k-th order array-variate data using k-self similar compound symmetry (k-SSCS) covariance structure is derived. The k-th order data appear in many scientific fields including agriculture, medical, environmental and engineering applications. We discuss the property of this k-SSCS covariance structure, namely, the property of Jordan algebra. We formally show that our D2 test statistic for k-th order data is an extension or the generalization of the D2 test statistic for second-order data and for third-order data, respectively. We also derive the D2 test statistic for third-order data and illustrate its application using a medical dataset from a clinical trial study of the eye disease glaucoma. The new test statistic is very efficient for high-dimensional data where the estimation of unstructured variance-covariance matrix is not feasible due to small sample size.

This paper proposes a novel method, based on a statistical probability distributional approach, Hotelling’s T2 statistic and Orthogonality test. If the input query image is structured, it is segmented into various regions according to its nature and structure. Otherwise, the image is treated as textured; and it is considered for the experiment as it is. The test statistic T2 is applied on each region and compares it to the target image. If the test of hypothesis is accepted, it is inferred that the query and target images are same or similar. Otherwise, it is assumed that they belong to different groups. Moreover, the Eigen vectors are computed on each region, and the orthogonality test is employed to measure the angle between the two images. The obtained results outperform the existing methods.

A new hypothesis testing of equality of mean vectors in two populations using D2 statistic for multivariate repeated measures data on q response variables at p sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only q+1, unlike pq+1 in Hotelling’s T2 test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the pq×pq dimensional unknown unstructured variance-covariance matrix. Some simulation studies are performed to compare the power of the new D2 test and the existing BT2 test. The performance of the proposed D2 test is demonstrated with the two medical data sets. [ABSTRACT FROM AUTHOR]

Profile monitoring is becoming popular in the area of quality control. It is used when the process is characterized by the relationship between a response variable and some explanatory variables at each time period. This paper considers the situation where profiles are modeled parametrically using a multiple linear regression with random errors following an autoregressive moving-average process. Diagnostic schemes to find out-of-control samples are developed for this purpose. A simulation study examines the performance of the proposed approach based on the average run length criterion. Lastly, a real example illustrates the results, after considering both Phase I and Phase II schemes. [ABSTRACT FROM AUTHOR]

This paper proposed and considered some bivariate control charts to monitor individual observations from a statistical process control. Usual control charts which use mean and variance-covariance estimators are sensitive to outliers. We consider the following robust alternatives to the classical Hoteling's T2: T2MedMAD, T2MCD, T2MVE a simulation study has been conducted to compare the performance of these control charts. Two real life data are analyzed to illustrate the application of these robust alternatives.

This paper proposes a novel method, based on a statistical probability distributional approach, Hotelling's T² statistic and Orthogonality test. If the input query image is structured, it is segmented into various regions according to its nature and structure. Otherwise, the image is treated as textured; and it is considered for the experiment as it is. The test statistic T² is applied on each region and compares it to the target image. If the test of hypothesis is accepted, it is inferred that the query and target images are same or similar. Otherwise, it is assumed that they belong to different groups. Moreover, the Eigen vectors are computed on each region, and the orthogonality test is employed to measure the angle between the two images. The obtained results outperform the existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider testing the equality of two mean vectors with unequal covariance matrices. In the case of equal covariance matrices, we can use Hotelling’sT2statistic, which follows theFdistribution under the null hypothesis. Meanwhile, in the case of unequal covariance matrices, theT2type test statistic does not follow theFdistribution, and it is also difficult to derive the exact distribution. In this paper, we propose an approximate solution to the problem by adjusting the degrees of freedom of theFdistribution. Asymptotic expansions up to the term of orderN− 2for the first and second moments of theUstatistic are given, whereNis the total sample size minus two. A new approximate degrees of freedom and its bias correction are obtained. Finally, numerical comparison is presented by a Monte Carlo simulation. [ABSTRACT FROM PUBLISHER]

Lately, profile monitoring has received considerable attention in the statistical process control research field. This paper proposes a novel monitoring framework for the reflow process data, which uses two goodness-of-fit criteria to select the change points in the mixture polynomial model. Among change points, the mixture second-order polynomials are utilized to piecewisely approximate the nonlinear profile data of the reflow process. The well-known Hotelling T2 and proposed EWMA4 control charts are then employed to monitor the parameter estimates. The experimental results demonstrate that the proposed monitoring framework presents better performances in detecting outlying profiles than the conventional methods in phase I. In phase II, the performance of the proposed framework is assessed in terms of the out-of-control average run length. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposed and considered some bivariate control charts to monitor individual observations from a statistical process control. Usual control charts which use mean and variance-covariance estimators are sensitive to outliers. We consider the following robust alternatives to the classical Hoteling's T2: T2MedMAD, T2MCD, T2MVE A simulation study has been conducted to compare the performance of these control charts. Two real life data are analyzed to illustrate the application of these robust alternatives. [ABSTRACT FROM AUTHOR]

Interpretation of out-of-control signals in multivariate control charts is a persistent problem. Identifying the variables contributing to the signal is of crucial importance for process control. Both procedures turn out to be more complicated when observations are compositions (variables adding to a constant sum). Compositional T2 control chart ( [ABSTRACT FROM AUTHOR]

The usual Hotelling T² control chart is not appropriate for monitoring processes where the quality characteristic is a mixture. The composition of mixtures are vectors of positive elements that represent parts of a whole, to which standard multivariate techniques are not appropriate due to their restricted sample space. There are many applications where a mixture is monitored against time, such as in the chemical industry, product composition, impurity profile, or gas components analysis. In this paper, a multivariate control chart for individual compositional observations based on the T² statistic is proposed and compared with the typical one in terms of average run length. We show how results are more consistent with compositional data nature and illustrate implementation in a real-world example. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new bivariate control chart denoted by [ABSTRACT FROM AUTHOR]

Multivariate monitoring techniques for serially correlated observations have been widely used in various applications. This study examines several issues that have arisen in relation to the statistical quality control for the vector autoregressive (VAR) model, using a Monte Carlo approach. Different versions of the Hotelling T2 statistic and control limits to monitor the VAR-type process for both Phase I and Phase II schemes can be specified for different sample sizes and configurations of the model. Our simulation study suggests that the Hotelling's T2 statistic can be tested against the χ2 critical values during Phase I, but should be tested against scaled F critical values during Phase II. An unbiased covariance estimate of residuals is also recommended during Phase II when sample size is typically small. By reanalyzing some real data examples, the authors offer new conclusions. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article presents a methodology for the diagnosis of abnormal conditions in a combustion process through flame imaging and kernel principal component analysis (KPCA). A digital imaging system is used to capture real-time flame images and radiation signals, from which flame characteristics such as flame area, brightness, non-uniformity, and oscillation frequency are quantified. These characteristics are used as the variables to establish the KPCA model of the combustion process. With the use of Hotelling's T2and Q statistics, the monitoring of abnormal conditions of the combustion process is achieved. Unlike the traditional principal component analysis (PCA) method, the KPCA method is capable of dealing with nonlinear data via nonlinear mapping, which projects the original nonlinear input space into a high-dimensional linear feature space. The effectiveness of the methodology is demonstrated by applying the approach to processing the data obtained on a 9MWthheavy oil fired combustion test facility. Experimental results obtained show that the KPCA method outperforms the traditional PCA in discriminating between the normal and abnormal combustion conditions, even in cases where the number of training samples is limited. [ABSTRACT FROM AUTHOR]

Poisson log-linear regression is a popular model for count responses. We examine two popular extensions of this model – the generalized estimating equations (GEE) and the generalized linear mixed-effects model (GLMM) – to longitudinal data analysis and complement the existing literature on characterizing the relationship between the two dueling paradigms in this setting. Unlike linear regression, the GEE and the GLMM carry significant conceptual and practical implications when applied to modeling count data. Our findings shed additional light on the differences between the two classes of models when used for count data. Our considerations are demonstrated by both real study and simulated data. [ABSTRACT FROM AUTHOR]

Partially paired data sets often occur in microarray experiments (Kim et al., 2005; Liu, Liang and Jang, 2006). Discussions of testing with partially paired data are found in the literature (Lin and Stivers 1974; Ekbohm, 1976; Bhoj, 1978). Bhoj (1978) initially proposed a test statistic that uses a convex combination of paired and unpaired t statistics. Kim et al. (2005) later proposed the t3 statistic, which is a linear combination of paired and unpaired t statistics, and then used it to detect differentially expressed (DE) genes in colorectal cancer (CRC) cDNA microarray data. In this paper, we extend Kim et al.'s t3 statistic to the Hotelling's T2 type statistic Tp for detecting DE gene sets of size p. We employ Efron's empirical null principle to incorporate inter-gene correlation in the estimation of the false discovery rate. Then, the proposed Tp statistic is applied to Kim et al's CRC data to detect the DE gene sets of sizes p=2 and p=3. Our results show that for small p, particularly for p=2 and marginally for p=3, the proposed Tp statistic compliments the univariate procedure by detecting additional DE genes that were undetected in the univariate test procedure. We also conduct a simulation study to demonstrate that Efron's empirical null principle is robust to the departure from the normal assumption. [ABSTRACT FROM AUTHOR]

The generalized estimating equations (GEEs) and generalized linear mixed-effects model (GLMM) are the two most popular paradigms to extend models for cross-sectional data to a longitudinal setting. Although the two approaches yield well-interpreted models for continuous outcomes, it is quite a different story when applied to binomial responses. We discuss major modeling differences between the GEE- and GLMM-derived models by presenting new results regarding the model-driven differences. Our results show that GLMM induces some artifacts in the marginal models at assessment times, making it inappropriate when applied to such responses from real study data. The different interpretations of parameters resulting from the conceptual difference between the two modeling approaches also carry quite significant implications and ramifications with respect to data and power analyses. Although a special case involving a scale difference in parameters between GEE and GLMM has been noted in the literature, its implications in real data analysis has not been thoroughly addressed. Further, this special case has a very limited covariate structure and does not apply to most real studies, especially multi-center clinical trials. The new results presented fill a substantial gap in the literature regarding the model-driven differences between the two dueling paradigms. [ABSTRACT FROM AUTHOR]

An extension of the D 2 test statistic to test the equality of mean for high-dimensional and k-th order array-variate data using k-self similar compound symmetry (k-SSCS) covariance structure is derived. The k-th order data appear in many scientific fields including agriculture, medical, environmental and engineering applications. We discuss the property of this k-SSCS covariance structure, namely, the property of Jordan algebra. We formally show that our D 2 test statistic for k-th order data is an extension or the generalization of the D 2 test statistic for second-order data and for third-order data, respectively. We also derive the D 2 test statistic for third-order data and illustrate its application using a medical dataset from a clinical trial study of the eye disease glaucoma. The new test statistic is very efficient for high-dimensional data where the estimation of unstructured variance-covariance matrix is not feasible due to small sample size. [ABSTRACT FROM AUTHOR]

Although most statistical process control techniques are designed to detect constant process shifts, time-varying shift patterns are more frequently encountered in industrial practice. In this paper, we propose an adaptive T² scheme for monitoring processes with dynamic shifts. The new scheme preserves the optimality of directionally variant charts by updating a reference mean-shift vector recursively and can be easily adjusted to obtain high sensitivity across desired shift ranges. Simulation studies show that the adaptive T² chart with EWMA forecasting of mean shifts outperforms most conventional charts in a dynamic environment and is also robust to parameter-estimation uncertainties. [ABSTRACT FROM AUTHOR]

The purpose of quality control charts is to detect abnormal behavior of quality variables and to determine the causes of quality problems using these abnormalities. Hotelling's T² charts, the most popular multivariate quality control charts, are used to monitor several quality variables, simultaneously. In this study, Hotelling's T² charts were applied to a melting process in a brass casting factory. A Hotelling's T² chart was formed from multivariate data collected from the process when it was in control; then, the chart was applied to new process data. Chart signals that are out of control limits were analyzed, and associated root causes were investigated in order to improve the process. Mason-Young-Tracy decomposition method was employed in this investigation. [ABSTRACT FROM AUTHOR]