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.

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.

<p>The multivariate cumulative sum (MCUSUM) and the multivariate exponentially weighted moving average (MEWMA) control charts are the two leading methods to monitor a multivariate process. This thesis focuses on the MEWMA control chart. Specifically, using the Markov chain method, we study in detail several aspects of the run length distribution both for the on- and off- target cases. Regarding the on-target run length analysis, we express the probability mass function of the run length distribution, the average run length (ARL), the variance of run length (V RL) and higher moments of the run length distribution in mathematically closed forms. In previous studies, with respect to the off-target performance for the MEWMA control chart, the process mean shift was usually assumed to take place at the beginning of the process. We extend the classical off-target case and introduce a generalization of the probability mass function of the run length distribution, the ARL and the V RL. What Prabhu and Runger (1996) proposed can be derived from our new model. By evaluating the off-target ARL values for the MEWMA control chart, we determine the optimal smoothing parameters by using the partition method that provides an easy algorithm to find the optimal smoothing parameters and study how they respond as the process mean shift time changes. We compare the ARL performance of the MEWMA control chart with that of the multivariate Shewhart control chart to see whether the MEWMA chart is still effective in detecting a small mean shift as the process mean shift time changes. In order to apply the model to semiconductor manufacturing processes, we use a bivariate normal distribution to generate sample data and compare the MEWMA control chart with the multivariate Shewhart control chart to evaluate how the MEWMA control chart behaves when a delayed mean shift happens. We also apply the variation transmission model introduced by Lawless et al. (1999) to the semiconductor manufacturing process and show an extension of the model to make our application to semiconductor manufacturing processes more realistic. All the programming and calculations were done in R</p> / Master of Science (MS)

"This Master’s capstone was conducted in conjunction with Draper Laboratory, a non-profit research and development organization in Cambridge, Massachusetts. During a three month period, the author worked for the Microfabrication Department, assisting with projects related to statistics and quality control. The author gained real-world experience in data collection and analysis, and learned a new statistical software. Statistical methods covered in this report include regression analysis, control charts and capability, Gage R & R studies, and basic exploratory data analysis."

Intrusion detection systems (IDS) have a vital role in protecting computer networks and information systems. In this thesis we applied an SPC monitoring concept to a certain type of traffic data in order to detect a network intrusion. We developed a general SPC intrusion detection approach and described it and the source and the preparation of data used in this thesis. We extracted sample data sets that represent various situations, calculated event intensities for each situation, and stored these sample data sets in the data repository for use in future research. A regular batch mean chart was used to remove the sample datas inherent 60-second cycles. However, this proved too slow in detecting a signal because the regular batch mean chart only monitored the statistic at the end of the batch. To gain faster results, a modified batch mean (MBM) chart was developed that met this goal. Subsequently, we developed the Modified Batch Mean Shewhart chart, the Modified Batch Mean Cusum chart, and the Modified Batch Mean EWMA chart and analyzed the performances of each one on simulated data. The simulation studies showed that the MBM charts perform especially well with large signals ?the type of signal typically associated with a DOS intrusion. The MBM Charts can be applied two ways: by using actual control limits or by using robust control limits. The actual control limits must be determined by simulation, but the robust control limits require nothing more than the use of the recommended limits. The robust MBM Shewhart chart was developed based on choosing appropriate values based on batch size. The robust MBM Cusum chart and robust MBM EWMA chart were developed on choosing appropriate values of charting parameters.

Statistical process control (SPC) which includes very powerful techniques used in other mature engineering disciplines for providing process control is not used by many software organizations. In software engineering domain, SPC is currently utilized only by organizations which have high maturity levels according to the process improvement models like CMM, ISO/IEC 15504 and CMMI. Guidelines and software tools to implement SPC techniques should be developed for effective use and dissemination of SPC especially for low maturity organizations. In this thesis, a software tool (SPC-AAT) which we developed to assess the suitability of software processes and metrics for SPC and use of SPC tools is presented. With SPC-AAT, we aim to ease and enhance application of SPC especially for emergent and low maturity organizations. Control charts, histograms, bar charts and pareto charts are the supported SPC tools for this purpose. We also explained the validation of the tool over two processes of a software organization in three case studies.

Volatility is an important measure of stock market performance. Competing securities market makers keep abreast of the pace of volatility change by adjusting the bid-ask spreads and bid/ask quotes properly and efficiently. For intradaily high frequency transaction data, the observed volatility of stock returns can be decomposed into the sum of the two components - the realized volatility and the volatility due to microstructure noise. The quote adjustments of the market makers comprise part of the microstructure noise. In this study, we define the ratio of the realized integrated volatility to the observed squared returns as the proportion of realized integrated volatility (PIV). Time series models with generalized error distributed innovations are fitted to the PIV data based on 70-minute returns of NYSE tick-to-tick transaction data. Both retrospective and dynamic online control charts of the PIV data are established based on the fitted time series models. The McNemar test supports that the dynamic online control charts have the same power of detecting out of control events as the retrospective control charts. The Wilcoxon signedrank test is adopted to test the differences between the changes of the market maker volatility and the realized volatility for in-control and out-of-control periods, respectively. The results reveals that the points above the upper control limit are related to the situation when the market makers can not keep up with the realized integrated volatility, whereas the points below the lower control limit indicate excessive reaction of the the market makers.

In the sawmill industry, it can be very profitable to monitor the dimensions of sawn boards so that operators quickly can detect errors and take cor-rective action. In this master’s thesis project, Statistical Process Control (SPC) methods have been implemented to achieve this. SPC is a set of statistical methods whose purpose is to minimize the variations in an in-dustrial process. In particular, the SPC method used here is the control chart, which with an upper and lower control limit quantifies the bounds of natural variation. To find the most suitable control chart, five control charts monitoring the process mean, and two monitoring process variability were tested with help of both a simulation study and an empirical evaluation. The result of the evaluation was that the ”Average Moving Range” chart was regarded the most suitable for changes in process mean, and the Range chart was regarded as the best at detecting changes in process variability. Both charts are constructed for individual boards and not subgroups of boards (as is more common) due to compatibility reasons with the existing measurement practice. The two methods were deemed to be quite able to detect process changes, but some results indicate that the methods might work better for double arbour saw lines than single arbour ones. / Det kan vara mycket lönsamt för sågverk att övervaka mått på plankor så att personal snabbt kan hitta och åtgärda fel som uppstår i processen. I det syftet har det här masterarbetet gått ut på att implementera statistisk processkontroll (SPC) för råmåttkontroll på sågverk. SPC är en mängd olika statistiska metoder vars syfte är att minimera spridningen i en tillverkningsprocess. Den metod som är i speciellt focus i det här arbetet är det så kallade styrdiagrammet som med en övre och undre gräns kvantifierar hur stor den naturligt förekommande spridningen är. För att finna det mest lämpade styrdiagrammet utvärderades fem styrdiagram som övervakar processens medelvärde och två styrdiagram som övervakar processens spridning. Denna utvärdering bestod både av en simuleringsstudie och tester gjorda för empiriskt data. Utvärderingen resulterade i att det så kallade ”Average Moving Range” diagrammet rekommenderades för övervakning av medelvärde och ett räckviddsstyrdiagram rekommenderades för spridningen. Båda styrdiagrammen konstruerades för enskilda plankor och inte för stickprov av flera plankor (vilket är vanligare) på grund av kompatibelitetsskäl med gängse mätmetodik. De båda metoderna ansågs vara ganska bra på att upptäcka processförändringar men vissa resultat tyder på att metoderna kanske fungerar bättre för sågverk med mötande klingor än enaxliga sågverk.