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L'objectif de cette thèse est le développement d'une méthodologie pour la détection de défauts appliquée aux équipements de production de semi-conducteurs. L'approche proposée repose sur l'Analyse en Composantes Principales (ACP) pour construire un modèle représentatif du fonctionnement nominal d'un équipement. Pour cela, notre méthodologie consiste à exploiter l'ensemble des mesures disponibles, collectées via les capteurs internes et externes au cours desopérations de fabrication pour chaque plaque manufacturée. Nous avons développé un module de pré-traitement permettant de transformer les mesures collectées en données interprétables par l'ACP, tout en filtrant l'information considérée comme non-désirable induite par la présence de valeurs aberrantes et perturbant la construction du modèle. Nous avons combiné des extensions de l'ACP linéaire et notamment l'ACP multiway, l'ACP filtrée ainsi que l'ACP récursive, de façon à adapter la modélisation aux caractéristiques des systèmes. L'utilisation d'un filtre par moyenne mobile exponentielle nous permet de considéré la dynamique du système au cours de la réalisation d'une opération. L'ACP récursive est employée pour adapter le modèle aux changements de comportement du système après certains événements (maintenance, redémarrage, etc.).Les différentes méthodes sont illustrées à l'aide de données réelles, collectées sur un équipement actuellement exploité par STMicroelectronics Rousset. Nous proposons également une application plus générale de la méthode pour différents types d'équipement et sur une période plus importante, de façon à montrer l'intérêt industriel et la performance de cette approche. / This thesis focus on developping a fault detection methodology for semiconductor manufacturing equipment. The proposed approach is based on Principal Components Analysis (PCA) to build a representative model of equipment in adequat operating conditions. Our method exploits collected measurements from equipement sensors, for each processed wafer. However, regarding the industrial context and processes, we have to consider additional problems: collected signals from sensors exhibit different length, or durations. This is a limitation considering PCA. We have also to consider synchronization and alignment problems; semiconductor manufacturing equipment are almost dynamic, with strong temporal correlations between sensor measurements all along processes. To solve the first point, we developped a data preprocessing module to transform raw data from sensors into a convenient dataset for PCA application. The interest is to identify outliers data and products, that can affect PCA modelling. This step is based on expert knowledge, statistical analysis, and Dynamic Time Warping, a well-known algorithm from signal processing. To solve the second point, we propose a combination multiway PCA with the use of an EWMA filter to consider process dynamic. A recursive approach is employed to adapt our PCA model to specific events that can occur on equipment, e.g. maintenance, restart, etc.All the steps of our methodology are illustrated with data from a chemical vapor deposition tool exploited in STMicroelectroics Rousset fab. Finally, the efficiency and industrial interest of the proposed methodologies are verified by considering multiple equipment types on longer operating periods.

Gráficos de controle têm sido amplamente utilizados na manufatura para melhoria de processos. Diversas abordagens tem sido propostas para melhorar o desempenho dos gráficos existentes na literatura. Além disso, o uso de gráficos de controle tem se estendido para outras áreas, tais como, economia, finanças, medicina, etc. O objetivo deste trabalho é comparar o gráfico CUSUM com o gráfico EWMA para monitoramento do número diário de internações hospitalares. Para tanto, utilizou-se uma série histórica de internações devido a doenças respiratórias para a população acima de 65 anos. Um modelo linear foi ajustado considerando que o número de internações segue uma distribuição Binomial Negativa. São simulados diversos cenários de mudança no número médio de internações e utilizando diferentes estatísticas baseadas em transformações, é feita uma comparação entre estes gráficos. Verifica-se que o gráfico EWMA com limite de controle assintótico possui desempenho muito similar ao gráfico CUSUM. Já o EWMA implementado com limite de controle exato apresenta melhor desempenho em relação ao gráfico CUSUM quando se atribui pesos menores aos dados atuais. / Control charts have been widely used for process improvement in manufacturing. In literature several approaches have been proposed to improve the current charts performance. In addition, the use of control charts has been extended to other areas such as economics, finance, medicine, and others. The objective of this study is to compare CUSUM control chart with EWMA control chart for monitoring daily number of hospital admissions. Using a historical hospitalizations series due to respiratory diseases for people over 65 years old, a Negative Binomial regression model is fitted. Several scenarios are simulated using different shifts in the mean and using different statistics based on transformations, in order to compare these charts. It is shown that EWMA control chart with asymptotic control limit has similar performance as CUSUM control chart. However, using smaller values for new observations the EWMA control chart with exact control limit has better performance than CUSUM control chart.

隨著經濟不斷的發展與進步，商品市場的需求漸趨多元，廠商彼此之間的競爭愈來愈激烈，為了滿足客戶多元的需求，採用多等級製程的生產方式成為廠商製造產品的一種策略。Doganaksoy, Schmee, and Vandeven (1996)提出使用EWMA管制圖監控多等級產品製程的方法，利用合併資料之EWMA管制圖可以更快速地偵測出同時影響所有等級產品品質特性之非機遇因素是否發生。但是他們並沒有考慮到管制圖的經濟層面，因此本文主要探討如何由經濟觀點設計EWMA管制圖以監控生產多等級產品的製程。 本研究所探討之多等級產品製程可生產二個等級產品。在同時影響所有等級產品品質特性之非機遇因素不存在的情況下，我們擴展Banerjee and Rahim(1987)的更新理論方法，建立了二個獨立的EWMA經濟管制圖；另外我們還討論管制圖在統計層面的表現，即以平均連串長度(ARL)為統計上的限制式，仿照經濟設計的做法，建立了二個獨立的EWMA經濟統計管制圖，並和經濟設計的結果做比較。最後我們考慮同時影響所有等級產品品質特性之非機遇因素發生在製程的情況下，擴展更新理論方法建立三個EWMA經濟管制圖以追蹤此製程狀態，文末並以例子說明如何使用EWMA經濟管制圖以監控多等級產品製程。 在資料分析方面，本研究考慮32組製程與成本參數組合，透過最佳化技巧找出EWMA經濟及經濟統計管制圖之最低成本及最佳設計參數組合。再利用敏感度分析，我們可以得知重要的製程與成本參數為何。這些訊息可做為製程工程師決策參考之用。 / With the progress of the economic of the world and the various demands of the consumers, there is a new strategy to product with multiple product grades. Doganaskoy, Schmee, and Vandeven(1996) had provided a method of using a combined exponentially weighted moving average (EWMA) control charts that allow speedy detection of assignable causes affecting all grades. But this control scheme is not designed from economic viewpoint. In this paper we will discuss how to construct an economic model for the EWMA control chart to monitor the process with multiple product grades. We discuss the process with two product grades. We expand the renewal theory method proposed by Banaerjee and Rahim (1987) to construct two independent economic EWMA control charts to monitor the process with two product grades. Besides, we also present a statistically constrained economic model of the EWMA control chart, subject to statistical constraints on average run length (ARL). If the assignable cause affecting all grades does exist, we also construct the three economic EWMA control charts by expanding the renewal theory approach. Finally, we illustrate how to use the economic EWMA control chart to monitor the process. In data analysis, 32 combinations of the cost and process parameters are considered. The minimum cost and the optimal design parameters of economical and economic statistical EWMA control charts are determined by using optimal techniques. Sensitivity analyses show the significant cost and process parameters.

Made available in DSpace on 2008-05-13T13:48:10Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-05-04 / The objective of this paper is to analyze the foreign reserves accumulation among countries such Brazil that builds up international reserves to be protected from externai crises as well as to diminish such probability. We desire to analyze also the determination of optimal levei of reserves. We will approach brief historical of the literature of reserves holdings. In the study of Brazil, we will discuss the optimal levei of Brazilian international reserves using buffer stock model, with temporaries series approach, differing from previous cross-section studies. / O objetivo deste trabalho analisar acumulação de reservas internacionais por parte de países como Brasil, que acumulam reservas na tentativa de se proteger de crises externas bem como diminuir tal probabilidade. Desejamos analisar determinação do nível ótimo de reservas. Apresentaremos um breve histórico da literatura sobre acumulação de reservas. No estudo do Brasil, discutiremos nível ótimo de reservas internacionais brasileiras usando modelo de buffer stock, partir de uma abordagem de séries temporais, diferindo de trabalhos anteriores usando dados cross-section.

Gráficos de controle têm sido amplamente utilizados na manufatura para melhoria de processos. Diversas abordagens tem sido propostas para melhorar o desempenho dos gráficos existentes na literatura. Além disso, o uso de gráficos de controle tem se estendido para outras áreas, tais como, economia, finanças, medicina, etc. O objetivo deste trabalho é comparar o gráfico CUSUM com o gráfico EWMA para monitoramento do número diário de internações hospitalares. Para tanto, utilizou-se uma série histórica de internações devido a doenças respiratórias para a população acima de 65 anos. Um modelo linear foi ajustado considerando que o número de internações segue uma distribuição Binomial Negativa. São simulados diversos cenários de mudança no número médio de internações e utilizando diferentes estatísticas baseadas em transformações, é feita uma comparação entre estes gráficos. Verifica-se que o gráfico EWMA com limite de controle assintótico possui desempenho muito similar ao gráfico CUSUM. Já o EWMA implementado com limite de controle exato apresenta melhor desempenho em relação ao gráfico CUSUM quando se atribui pesos menores aos dados atuais. / Control charts have been widely used for process improvement in manufacturing. In literature several approaches have been proposed to improve the current charts performance. In addition, the use of control charts has been extended to other areas such as economics, finance, medicine, and others. The objective of this study is to compare CUSUM control chart with EWMA control chart for monitoring daily number of hospital admissions. Using a historical hospitalizations series due to respiratory diseases for people over 65 years old, a Negative Binomial regression model is fitted. Several scenarios are simulated using different shifts in the mean and using different statistics based on transformations, in order to compare these charts. It is shown that EWMA control chart with asymptotic control limit has similar performance as CUSUM control chart. However, using smaller values for new observations the EWMA control chart with exact control limit has better performance than CUSUM control chart.

This diploma thesis deals with the evaluation of the capability of a specific production process. The theoretical part of the work contains a description of statistical process control, types of control charts and evaluation of process capability. The practical part is focused on evaluating the capability of a specific process. The method of dataset collection is described at first, then this data are analyzed and the capability of this process is evaluated.

In thesis within Industrial Economics and Applied Mathematics in cooperation with Svenska Handelsbanken given transformations was examined in order to assess their ability to make a given time series stationary. In addition, a parameter α belonging to each of the transformation formulas was to be decided. To do this an extensive study of previous research was conducted and two different tests of hypothesis where obtained to confirm output. A result was concluded where a value or interval for α was chosen for each transformation. Moreover, the first difference transformation is proven to have a positive effect on stationarity of financial data. / Det här kandidatexamensarbetet inom Industriell Ekonomi och tillämpad matematik i samarbete med Handelsbanken undersöker givna transformationer för att bedöma deras förmåga att göra givna tidsserier stationära. Dessutom skulle en parameter α tillhörande varje transformations formel bestämmas. För att göra detta utfördes en omfattande studie av tidigare forskning och två olika hypotestester gjordes för att bekräfta output. Ett resultat sammanställdes där ett värde eller ett intervall för α valdes till varje transformation. Dessutom visade det sig att "first difference" transformationen är bra för stationäritet av finansiell data.

Control charts are used to effectively monitor and determine whether a process is in-control or out-of-control. The properties of EWMA control charts on a single process have been discussed by many researchers. They have proved that EWMA control charts detect small shifts in means or variances more quickly than the traditional Shewhart control charts. However, many products are currently produced in several dependent process steps. In this article, (1) we propose three kinds of EWMA control charts, - , - , and a combined control charts, to monitor the process mean and variance for a single process step, and (2) extend the three kinds of EWMA control charts in (1) to control two dependent steps. The performance of the proposed control charts is measured by using the Markov chain approach. The application of the proposed control charts is illustrated by using some numerical examples, and the performance of the proposed charts is compared by using some numerical examples. The adjusted average time to signal (AATS) and the adjusted average samples to signal (ANOS) are calculated to measure the performance of the proposed EWMA control charts by Markov chain approach. A data set consisting of the measurements of the inside diameter of the cylinder bores in an engine block example illustrates the applications of the three kinds of EWMA control charts for a single step and a empirical automobile braking system example illustrates the applications of the three kinds of EWMA control charts for two dependent steps. Moreover, their performances are compared by some numerical analysis results.

Recently, in the health surveillance area, control charts have been proposed to decide if the morbidity or mortality of a specific disease reached an epidemic level. This thesis is composed by 3 papers. In the first two papers, CUSUM and EWMA control charts were proposed to monitor count time series with seasonal and trend effects using the Generalized Autoregressive and Moving Average models (GARMA), instead of the independent Generalized Linear Model (GLM) as it is usually used in practice. Different statistics based on transformations, for variables that follow a Negative Binomial distribution, were used in these control charts. In the second paper, two new statistics were proposed based on the ratio of log-likelihood function. Different scenarios describing disease profiles were considered to evaluate the effect of omission of serial correlation in EWMA and CUSUM control charts. The performance of CUSUM and EWMA charts when the serial correlation is neglected in the regression model was measure in terms of average run length (ARL). In summary, when the autocorrelation is neglected, fitting a pure GLM instead of a GARMA model will lead to an increase of false alarms. However, no statistics among the tested ones seem to be robust, in a sense to produce the smallest increase of false alarms in all scenarios. In general, all monitored statistics presented a smaller ARL_0 for higher values of autocorrelation. \\\\ In the last paper, the GARMA models (p, q) with p and q simultaneously different from zero were studied since that two features were observed in practice. One is the multicollinearity, which may lead to a non-convergence of the maximum likelihood, using iteratively reweighted least squares. The second is the inclusion of the same lagged observations into the autoregressive and moving average components confounding the interpretation of the parameters. In a general sense, simulation studies show that the modified model provide estimators closer to the parameters and offer confidence intervals with higher coverage percentage than obtained with the GARMA model, but some restrictions in the parametric space are imposed to guarantee the stationarity of the process. Also, a real data analysis illustrate the GARMA-M fit for daily hospilatization rates of elderly people due to respiratory diseases from October 2012 to April 2015 in São Paulo city, Brazil. / Recentemente, no campo da saúde, gráficos de controle têm sido propostos para monitorar a morbidade ou a mortalidade decorrentes de doenças. Este trabalho está composto por três artigos. Nos dois primeiros artigos, gráficos de controle CUSUM e EWMA foram propostos para monitorar séries temporais de contagens com efeitos sazonais e de tendência usando os modelos Generalized autoregressive and moving average models (GARMA), em vez dos modelos lineares generalizados (GLM), como usualmente são utilizados na prática. Diferentes estatísticas baseadas em transformações, para variávies que seguem uma distribuição Binomial Negativa, foram usadas nestes gráficos de controle. No segundo artigo foram propostas duas novas estatísticas baseadas na razão da função de log-verossimilhança. Diferentes cenários que descrevem perfis de doenças foram considerados para avaliar o efeito da omissão da correlação serial nesses gráficos de controle. Este impacto foi medido em termos do Average Run Lenght (ARL). Notou-se que a negligência da correlação serial induz um aumento de falsos alarmes. Em geral, todas as estatísticas monitoradas apresentaram menores valores de ARL_0 para maiores valores de autocorrelação. No entanto, nenhuma estatística entre as consideradas mostrou ser mais robusta, no sentido de produzir o menor aumento de falsos alarmes nos cenários considerados. No último artigo, foram estudados os modelos GARMA (p, q) com p e q simultaneamente diferentes de zero, uma vez que duas características foram observadas na prática. A primeira é a presença de multicolinearidade, que induz à não-convergência do método de máxima verossimilhança usando mínimos quadrados ponderados reiterados. A segunda é a inclusão dos mesmos termos defasados nos componentes autorregressivos e de médias móveis. Um modelo modificado, GARMA-M, foi apresentado para lidar com a multicolinearidade e melhorar a interpretação dos parâmetros. Em sentido geral, estudos de simulação mostraram que o modelo modificado fornece estimativas mais próximas dos parâmetros e intervalos de confiança com uma cobertura percentual maior do que a obtida nos modelos GARMA. No entanto, algumas restrições no espaço paramétrico são impostas para garantir a estacionariedade do processo. Por último, uma análise de dados reais ilustra o ajuste do modelo GARMA-M para o número de internações diárias de idosos devido a doenças respiratórias de outubro de 2012 a abril de 2015 na cidade de São Paulo, Brasil.