Copula functions represent a methodology which can describe the dependence structure of multi-dimension random variable, and has recently become the most significant new tool to handle risk factors in finance such as Value-at Risk( VaR) which was probably the most widely used risk measure in financial institutions. In this paper, Copula and the forecast function of Garch model are well combined, and a new method Conditional-Copula-Garch is built for measure the dependence of financial data and compute the VaR of portfolios. Copula-Garch models allow for very flexible joint distribution by splitting the marginal behaviors form the dependence relation unlike the traditional approaches for the estimation VaR, such as variance-covariance, and the Monte Carlo approaches whereas demand the joint distribution to be known. This work presents an application of the Copula-Garch model in the estimation of VaR of a portfolio composed by NASDAQ and TAIEX (Taiwan stock exchanged capitalization weighted index) stock indices.

Statistical quality control charts originated in the late 1920’s by Shewhart (1926, 1931 and 1939). Their applications in various disciplines have been ever-increasing. Although most control charts are distribution-based, recent literature witnessed the development of a considerable number of distribution-free or nonparametric control charts. The purpose of this thesis is to present the concepts and introduce the researcher to the essentials of univariate nonparametric control charts. Various properties of nonparametric control charts are comprehensively discussed and concepts are clearly explained. Proofs and detailed calculations have been given to help the reader to study and understand the subject more thoroughly. This text contains a wide variety of illustrative examples to give an overall picture of how nonparametric control charts are used. Both simulated and real data examples have been integrated throughout the text. Since most practical problems are too large to be solved using hand calculations, some type of statistical software package is required to solve these problems. There are several excellent statistical packages available and in this thesis we make use of Microsoft Excel, SAS, Minitab, Mathcad and Mathematica to construct (almost all) the tables in this thesis. We point out that a number of Mathematica programs are provided by Chakraborti and Van de Wiel (2003) by means of the website www.win.tue.nl/~markvdw. The aim throughout is to convey the concepts of univariate nonparametric control charts in a way that readers will find attractive and interesting. Since the majority of nonparametric procedures, to be distribution-free, require a continuous population, only variables control charts are covered. We only consider control charts for monitoring the location of a process, since very few nonparametric charts are available for monitoring the spread. In this thesis we consider the three main classes of control charts: the Shewhart, CUSUM and EWMA control charts and their refinements. The text is divided into several chapters. An introduction to nonparametric control charts is presented in Chapter 1. A discussion of some of the advantages of nonparametric control charts is included while pointing out some of the disadvantages. In Chapter 2 we describe the Shewhart-, CUSUMand EWMA-type sign control charts with (and without) warning limits. In Chapter 3 we describe the Shewhart-, CUSUM- and EWMA-type signed-rank control charts with (and without) runs-type signalling rules. The Shewhart-type sign-like control chart with (and without) signalling rules is considered in Chapter 4. In Chapter 5 we consider the Shewharttype signed-rank-like control chart. Finally, in Chapter 6 we consider the Shewhart- and CUSUM-type Mann-Whitney-Wilcoxon control charts. We considered decision problems under both Phase I and Phase II (see Section 1.5 for a distinction between the two phases). In all the sections of this thesis we considered Phase II process monitoring, except in Section 6.2 where a CUSUM-type control chart for the preliminary Phase I analysis of individual observations based on the Mann-Whitney two-sample test is proposed. In the last chapter we have some concluding remarks along with some ideas for future research. / Dissertation (MSc)--University of Pretoria, 2011. / Statistics / unrestricted

Masivní vývoj Internetu vedl ke zvýšeným požadavkům na spolehlivou síťovou infrastrukturu. Efektivita komunikace v síti závisí na schopnosti směrovačů určit nejlepší cestu pro odesílání a přeposílání paketů ke koncovému zařízení. Jelikož OSPF v současné době představuje jeden z nejpoužívanějších směrovacích protokolů, jakýkoli přínos, který by pomohl udržet krok s rychle se měnícím prostředí Internetu, je velmi vítán. Významným omezením OSPF protokolu je, mimo jiné, absence informovanosti algoritmu pro výpočet metriky o aktuálním vytížení linky. Tato vlastnost představuje tzv. slabé místo, což má negativní vliv na výkonnost sítě. Z tohoto důvodu byla navržena nová metoda založená na dynamické adaptaci měnících se síťových podmínek a alternativní strategii OSPF metrik. Navržená metoda řeší problém neinformovanosti OSPF metriky o síťovém provozu a nevhodně vytížených linek, které snižují výkonnost sítě. Práce rovněž přináší praktickou realizaci, kdy vlastnosti nové metody jsou testovány a ověřeny spuštěním testů algoritmu v reálných zařízeních.

Empresa Brasileira de Pesquisa Agropecuária / This study used the data from a tobacco company that monitors its production process through statistical process control. The objective of this study was to apply multivariate statistical tools of Statistical Process Control to monitor the efficiency of the production process of the company under study. This production process consists of four variables monitored during the manufacture of cigarettes: RDT (Resistence to Draw), weight, ventilation and circunference. These data were verified using descriptive statistics, test of normality, univariate R and X-bar charts and correlation matrix. After observing the instability of the system, the Principal Component Analysis (PCA) was applied. PCA is an exploratory multivariate analysis technique that aims at gathering various features of the significant variables in the instability of the production process. EWMA was then applied on the principal components. An unstable process presenting too much variability was observed, with several points outside the bounds of statistical control. This situation presents some problems that may cause inconvenience and loss to the company. This way, the company should review its manufacturing process in order to improve its productivity and quality that in turn may help the company to be more competitive. / O presente estudo utilizou-se dos dados de uma empresa fumageira que monitora o processo produtivo por meio do controle estatístico do processo. Objetivou-se a aplicação de ferramentas estatísticas multivariadas de Controle Estatístico do Processo, para monitorar a eficiência do processo produtivo da empresa em estudo. Esse processo produtivo é composto de quatro variáveis, monitoradas na fase de fabricação do cigarro, sendo: RDT (Resistence to Draw), peso, ventilação e circunferência. Esses dados foram verificados através da estatística descritiva, Teste de Normalidade, gráficos univariados X-barra e R, e Matriz de correlação. Após constatada a instabilidade do sistema, aplicou-se Análise de Componentes Principais ACP, técnica de análise exploratória multivariada com o objetivo de aglutinar várias características das variáveis significativas na instabilidade do processo produtivo. Por último, foi aplicado EWMA (Exponentially Weighted Moving Average - Médias Móveis Exponencialmente Ponderáveis) sobre as componentes principais. Demonstrou-se um processo instável, apresentando muita variabilidade, com muitos pontos fora dos limites de controle estatístico. Essa situação, apresenta alguns problemas, que geram transtornos e prejuízos à empresa, sendo que a mesma deverá rever seu processo fabril a fim de melhorar a produtividade e a qualidade, que contribuirá para tornar a empresa mais competitiva.

無 / In this article, a two-step process is considered to investigate the effects of measurement errors on EWMA and cause-selecting EWMA control charts. At the end of current process, a pair of imprecise measurements of in-coming quality and out-going quality is randomly taken with individual units. The linear relationship between in-coming quality and out-going quality is assumed and four possible states of the process are defined with respective distributions of in-coming and out-going qualities derived. The EWMA control chart with measurement error is then constructed to monitor small-scale shift in mean for the previous process while the cause-selecting control chart, or EWMA control chart based on residuals, including measurement error, is proposed to diagnose the state of current process. Based on sensitivity analysis, the presence of imprecise measurement diminishes the power of both the EWMA and the proposed control charts and affects the detectability of process disturbances. Further, applications of proposed control charts are demonstrated through a numerical example to show some possible misuses of control charts. If the process mean shifts in a small scale when a single assignable cause occurs on each step, the proposed cause-selecting control chart is more sensitive than other control charts. The Hotelling T^2 control chart is also compared to illustrate the diagnostic advantage outweighed by proposed cause-selecting control chart.

<p>When flying a fighter aircraft such as the JAS 39 Gripen, the pilot is exposed to high g-loads. In order to prevent the draining of blood from the brain during this stress an anti-g protection system is used. The system consists of a pair of trousers, called the anti-g trousers, with inflatable bladders. The bladders are filled with air, pressing tightly on to the legs in order to prevent the blood from leaving the upper part of the body.</p><p>The purpose of this thesis is to detect if the pressure of the anti-g trousers is deviating from the desired value. This is done by developing a detection algorithm which gives two kinds of alarm. One is given during minor deviations using a CUSUM test, and one is given at grave deviations, based on different conditions including residual, derivative and time. The thresholds, in which between the pressure should lie in a faultless system, are calculated from the g-load value. The thresholds are based upon given static guidelines for the pressure tolerance area and are modified in order to adapt to the estimated dynamics of the system.</p><p>The values of the input signals, pressure and g-load, were taken from real flight sessions. The validation has been performed using both faultless and faulty flight sequences, with low false alarm rate and no missed detections. All together the detection system is considered to work well.</p>

Long range dependent processes occur in many fields, it is important to monitor these processes to early detect their shifts. This paper considers the problem of detecting changes in an I(d) process or an ARFIMA(p,d,q) process by statistical control charts. The control limits of EWMA and EWRMS control charts of I(d) processes are established and analytic forms are derived. The average run lengths of these control charts are estimated by Monte Carlo simulations. In addition, we illustrate the performance of the control charts by empirical examples of I(d) processes and ARFIMA(1,d,1) processes.

Zugl.: Karlsruhe, Universiẗat, Diss., 2009.

Industrial processes are subject to changes that can adversely affect product quality. A change in the process that increases the variability of the output of the process causes the output to be less uniform and increases the probability that individual items will not meet specifications. Statistical control charts for monitoring process variance can be used to detect an increase in the variability of the output of a process so that the situation can be repaired and product uniformity restored. Control charts that increase the sampling rate when there is evidence the variance has changed gather information more quickly and detect changes in the variance more quickly (on average) than fixed sampling rate procedures. Several variable sampling rate procedures for detecting increases in the process variance will be developed and compared with fixed sampling rate methods. A control chart for the variance is usually used with a separate control chart for the mean so that changes in the average level of the process and the variability of the process can both be detected. A simple method for applying variable sampling rate techniques to dual monitoring of mean and variance will be developed. This control chart procedure increases the sampling rate when there is evidence the mean or variance has changed so that changes in either parameter that will negatively impact product quality will be detected quickly. / Ph. D.

Traditional control charts for process monitoring are based on taking samples from the process at regular time intervals. However, it is often possible in practice for observations, and even entire samples, to be missing. This dissertation investigates missing observations in Exponentially Weighted Moving Average (EWMA) and Multivariate EWMA (MEWMA) control charts. The standardized sample mean is used since this adjusts the sample mean for the fact that part of the sample may be missing. It also allows for constant control limits even though the sample size varies randomly. When complete samples are missing, the weights between samples should also be adjusted. In the univariate case, three approaches for adjusting the weights of the EWMA control statistic are investigated: (1) ignoring missing samples; (2) adding the weights from previous consecutive missing samples to the current sample; and (3) increasing the weights of non-missing samples in proportion, so that the weights sum to one. Integral equation and Markov chain methods are developed to find and compare the statistical properties of these charts. The EI chart, which adjusts the weights by ignoring the missing samples, has the best overall performance. The multivariate case in which information on some of the variables is missing is also examined using MEWMA charts. Two methods for adjusting the weights of the MEWMA control statistic are investigated and compared using simulation: (1) ignoring all the data at a sampling point if the data for at least one variable is missing; and (2) using the previous EWMA value for any variable for which all the data are missing. Both of these methods are examined when the in-control covariance matrix is adjusted at each sampling point to account for missing observations, and when it is not adjusted. The MS control chart, which uses the previous value of the EWMA statistic for a variable if all of the data for that variable is missing at a sampling point, provides the best overall performance. The in-control covariance matrix needs to be adjusted at each sampling point, unless the variables are independent or only weakly correlated. / Ph. D.