An Explanatory Study on the Non-Parametric Multivariate T2 Control Chart

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T2 are correlated, the T2 chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is presented based on Hotelling’s T2 statistic then the performance of the bootstrap multivariate control chart is compared to a Hotelling’s T2 parametric multivariate control chart, a multivariate sign control chart, and a multivariate Wilcoxon control chart using a simulation study. Ultimately, the bootstrap multivariate control chart is used in an empirical example to study the process of sugar production

Online monitoring of dynamic networks using flexible multivariate control charts

The identification of differences in dynamic networks between various time points is an important task and involves statistical procedures like two-sample tests or changepoint detection. Due to the rather complex nature of temporal graphs, the analysis is challenging which is why the complexity is typically reduced to a metric or some sort of a model. This is not only likely to result in a loss of relevant information, but common approaches also use restrictive assumptions and are therefore heavily limited in their usability. We propose an online monitoring approach usable for flexible network structures and able to handle various types of changes. It is based on a sound choice of a set of network characteristics under consideration of their mathematical properties which is crucial in order to cover the relevant information. Subsequently, those metrics are jointly monitored in a suitable multivariate control chart scheme which performs superior to a univariate analysis and enables both parametric and non-parametric usage. The user also benefits from a handy interpretation of the structural reasons for the detected changes which is a crucial advantage in the rather complex field of dynamic networks. Our findings are supported by an extensive simulation study

A comparison study of distribution-free multivariate SPC methods for multimode data

The data-rich environments of industrial applications lead to large amounts of correlated quality characteristics that are monitored using Multivariate Statistical Process Control (MSPC) tools. These variables usually represent heterogeneous quantities that originate from one or multiple sensors and are acquired with different sampling parameters. In this framework, any assumptions relative to the underlying statistical distribution may not be appropriate, and conventional MSPC methods may deliver unacceptable performances. In addition, in many practical applications, the process switches from one operating mode to a different one, leading to a stream of multimode data. Various nonparametric approaches have been proposed for the design of multivariate control charts, but the monitoring of multimode processes remains a challenge for most of them. In this study, we investigate the use of distribution-free MSPC methods based on statistical learning tools. In this work, we compared the kernel distance-based control chart (K-chart) based on a one-class-classification variant of support vector machines and a fuzzy neural network method based on the adaptive resonance theory. The performances of the two methods were evaluated using both Monte Carlo simulations and real industrial data. The simulated scenarios include different types of out-of-control conditions to highlight the advantages and disadvantages of the two methods. Real data acquired during a roll grinding process provide a framework for the assessment of the practical applicability of these methods in multimode industrial applications

Nonparametric (distribution-free) control charts : an updated overview and some results

Control charts that are based on assumption(s) of a specific form for the underlying process distribution are referred to as parametric control charts. There are many applications where there is insufficient information to justify such assumption(s) and, consequently, control charting techniques with a minimal set of distributional assumption requirements are in high demand. To this end, nonparametric or distribution-free control charts have been proposed in recent years. The charts have stable in-control properties, are robust against outliers and can be surprisingly efficient in comparison with their parametric counterparts. Chakraborti and some of his colleagues provided review papers on nonparametric control charts in 2001, 2007 and 2011, respectively. These papers have been received with considerable interest and attention by the community. However, the literature on nonparametric statistical process/quality control/monitoring has grown exponentially and because of this rapid growth, an update is deemed necessary. In this article, we bring these reviews forward to 2017, discussing some of the latest developments in the area. Moreover, unlike the past reviews, which did not include the multivariate charts, here we review both univariate and multivariate nonparametric control charts. We end with some concluding remarks.https://www.tandfonline.com/loi/lqen20hj2020Science, Mathematics and Technology Educatio

Obtenção de limites estatísticos de controle em gráficos de controle univariados e multivariados aplicados a dados de instrumentação de barragens

Orientadora : Profª. Drª. Liliana Madalena GramaniCo-orientador : Prof. Dr. Anselmo Chaves NetoCo-orientador : Prof. Dr. Luiz Albino Teixeira JuniorTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 11/03/2016Inclui referências : f. 199-209Área de concentração : Programação matemáticaResumo: Barragens instrumentadas geram uma enorme base de dados provenientes do monitoramento. Porém, dados não são informações e, então, precisam ser trabalhados para se obter informações. A correta interpretação e avaliação da informação contida nos dados podem ser extremamente úteis para o acompanhamento do período operacional de uma barragem. O controle estatístico de qualidade univariado e multivariado é uma abordagem que pode contribuir com a descoberta de conhecimento em dados de instrumentos de monitoramento de barragens, sobretudo quando há correlação e quando não se tem informação sobre o comportamento das séries temporais de monitoramento dos instrumentos. Enquanto que gráficos de controle univariados são aplicados, há quase um século, no controle de características de qualidade, propostas multivariadas e modelos aplicados em segurança de barragens têm ainda poucos trabalhos publicados e têm se mostrado promissoras. Por outro lado, no caso univariado, o avanço da informática permitiu a execução de novas técnicas para modelar e realizar previsões em séries temporais, em particular, a combinação de técnicas com modelos ARIMA, ARIMAX-GARCH, decomposição Wavelet e Redes Neurais Artificiais tem mostrado melhoria no desempenho da previsão. O objetivo principal deste estudo é aplicar técnicas estatísticas univariadas e multivariadas, combinadas com outras técnicas paramétricas e não paramétricas aos dados de instrumentação de barragens a fim de desenvolver modelos capazes de estabelecer valores estatísticos de controle e previsões às séries temporais de leituras de instrumentos para a avaliação do desempenho futuro de uma barragem. Os modelos desenvolvidos foram testados e validados nos dados de instrumentos do trecho E da Usina Hidrelétrica de Itaipu Binacional, localizada no Rio Paraná, entre o Brasil e o Paraguai. Os resultados mostraram que o gráfico multivariado ???? das componentes principais combinado com os modelos ARIMAX-GARCH e técnicas não paramétricas permitem manter as taxas de falsos alarmes muito mais próximas do valor esperado em relação aos gráficos univariados e ???? multivariados, quando se presume normalidade nos dados. Além disso, a utilização de modelos híbridos, que combinam a decomposição Wavelet, a modelagem ARIMA-GARCH e Redes Neurais Artificiais pode melhorar o desempenho da previsão da série temporal da leitura de um instrumento comparativamente à utilização individualizada destas técnicas.Abstract: Dams with instruments generate a huge base of data from the monitoring. However, data is not information, and then need to be work to obtain information. The correct interpretation and evaluation of the information contained in the data can be extremely useful for monitoring the operational period of a dam. The univariate and multivariate statistical quality control is an approach that can contribute to knowledge discovery in data dam monitoring instruments, especially when there is correlation and when there is no information on the behavior of time series of monitoring instruments. While univariate control charts are applied for nearly a century in the quality control of characteristics, multivariate proposals and models applied in dam safety still have few papers published and have proven to be promising. On the other hand, in the univariate case, the advance of computer technology has allowed the implementation of new techniques to model and make predictions in time series, in particular, the combination of techniques ARIMA models ARIMAX-GARCH, Wavelet decomposition and artificial neural networks has shown improved performance of the forecast. The main goal of this study is to apply univariate and multivariate statistics techniques, combined with other parametric and nonparametric techniques to dam instrumentation data to develop models able to establish statistical control values and forecast the time series of instrument readings for assessment of the future performance of a dam. The developed models have been tested and validated on data from instruments of the E section of the Binational Itaipu hydroelectric plant, located on the Paraná River, between Brazil and Paraguay. The results showed that the multivariate graphic ???? of the principal components combined with ARIMAX-GARCH and nonparametric techniques allows to maintain the rates of false alarms much closer of the expected value in relation to the univariate graphs and ???? multivariate, when data are assumed to be normal. Furthermore, the use of hybrid models that combine the Wavelet decomposition, ARIMA-GARCH modeling and artificial neural networks can improve time-series forecasting performance of an instrument reading compared to the individual use of these techniques