Our objective is to monitor the changes in a proportion with correlated binary observations. All of the published work on this subject used the first-order Markov chain model for the data. Increasing the order of dependence above one by extending a standard Markov chain model entails an exponential increase of both the number of parameters and the dimension of the transition probability matrix. In this dissertation, we develop a particular Markov chain structure, the Multilevel Model (MLM), to model the correlation between binary data. The basic idea is to assign a lower probability to observing a 1 when all previous correlated observations are 0's, and a higher probability to observing a 1 as the last observed 1 gets closer to the current observation. We refer to each of the distinct situations of observing a 1 as a "level". For a given order of dependence, , at most different values of conditional probabilities of observing a 1 can be assigned. So the number of levels is always less than or equal to . Compared to a direct extension of the first-order Markov model to higher orders, our model is considerably parsimonious. The number of parameters for the MLM is only one plus the number of levels, and the transition probability matrix is . We construct a CUSUM control chart for monitoring a proportion with correlated binary observations. First, we use the probability structure of a first-order Markov chain to derive a log-likelihood ratio based CUSUM control statistic. Then, we model this CUSUM statistic itself as a Markov chain, which in turn allows for designing a control chart with specified statistical properties: the Markov Binary CUSUM (MBCUSUM) chart. We generalize the MBCUSUM to account for any order of dependence between binary observations through implying MLM to the data and to our CUSUM control statistic. We verify that the MBCUSUM has a better performance than a curtailed Shewhart chart. Also, we show that except for extremely large changes in the proportion (of interest) the MBCUSUM control chart detects the changes faster than the Bernoulli CUSUM control chart, which is designed for independent observations. / Ph. D.

Many performance measurement algorithms can only evaluate measure active managers' performance after a period of operating time. However, most investors are interested in monitoring the active managers' performances at any time, especially, when the performance is going down. So that the investors can adjust the targets and contents of their portfolios to reduce their risks. Yashchin,Thomas and David (1997) proposed to use a statistical quality control (SQC) procedure to monitor active managers' performances. In particular, they established the IR (Information Ratio) control charts under normality assumption to monitor the dynamic performances of active managers. However, the distributions of IR statistic usually possess fat tail property. Since the underlying distribution of IR is an important hypothesis in building up the control chart, we consider the heavy tail distributions, such as mixture normal and generalized error distribution to fit the IR data. Based on the fitted distribution, the IR control charts are rebuilt. By simulations and empirical studies, the remedial control charts are found to detect the shifts of active managers' performances more sensitively.

Count data are often encountered in manufacturing and service industries due to ease of data collection. These counts can be useful in process monitoring to detect shifts of a process from an in-control state to various out-of-control states. It is usually assumed that the observations are independent and identically distributed. However, in practice, observations may be autocorrelated and this may adversely affect the performance of the control charts developed under the assumption of independence. In this thesis, the cumulative sum (CUSUM) control chart for monitoring autocorrelated processes of counts is investigated. To describe the autocorrelation structure of counts, a Poisson integer-valued autoregressive moving average model of order 1, Poisson INAR(1), is employed. Changes in the process mean in both positive and negative directions are taken into account while designing the CUSUM chart. A trivariate Markov Chain approach is utilized for evaluating the performance of the chart.

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.

Taiwan Security Market is a typical order-driven market. The electronic trading system of Taiwan Security Market launched in 1998 significantly reduces the trade matching time (the current matching time is around 20 seconds) and promptly provides updated online trading information to traders. In this study, we establish an online transaction simulation system which can be applied to predict trade prices and study market efficiency. Models are established for the times and volumes of the newly added bid/ask orders on the match list. Exponentially weighted moving average (EWMA) method is adopted to update the model parameters. Match prices are predicted dynamically based on the EWMA updated models. Further, high frequency bid/ask order data are used to find the supply and demand curves as well as the equilibrium prices. Differences between the transaction prices and the equilibrium prices are used to investigate the efficiency of Taiwan Security Market. Finally, EWMA and cusum control charts are used to monitor the market efficiency. In empirical study, we analyze the intra-daily (April, 2005) high frequency match data of Uni-president Enterprises Corporation and Formosa Plastics Corporation.

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.

The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process. / The CUSUM control charts have been widely used in detecting small process shifts since it was first introduced by Page (1954). And recent studies have shown that adaptive charts can improve the efficiency and performance of traditional Shewhart charts. To monitor the process mean and variance in a single chart, the loss function is used as a measure statistic in this article. The loss function can measure the process quality loss while the process mean and/or variance has shifted. This study combines the three features: adaption, CUSUM and the loss function, and proposes the optimal VSSI, VSI, and FP CUSUM Loss chart. The performance of the proposed charts is measured by using Average Time to Signal (ATS) and Average Number of Observations to Signal (ANOS). The ATS and ANOS calculations are based on Markov chain approach. The performance comparisons between the proposed charts and some existing charts, such as X-bar+S^2 charts and CUSUM X-bar+S^2 charts, are illustrated by numerical analyses and some examples. From the results of the numerical analyses, it shows that the optimal VSSI CUSUM Loss chart has better performance than the optimal VSI CUSUM Loss chart, optimal FP CUSUM Loss chart, CUSUM X-bar+S^2 charts and X-bar+S^2 charts. Furthermore, using a single chart to monitor a process is not only easier but more efficient than using two charts simultaneously. Hence, the adaptive CUSUM Loss charts are recommended in real process.