abstract: There has been much research involving simultaneous monitoring of several correlated quality characteristics that rely on the assumptions of multivariate normality and independence. In real world applications, these assumptions are not always met, particularly when small counts are of interest. In general, the use of normal approximation to the Poisson distribution seems to be justified when the Poisson means are large enough. A new two-sided Multivariate Poisson Exponentially Weighted Moving Average (MPEWMA) control chart is proposed, and the control limits are directly derived from the multivariate Poisson distribution. The MPEWMA and the conventional Multivariate Exponentially Weighted Moving Average (MEWMA) charts are evaluated by using the multivariate Poisson framework. The MPEWMA chart outperforms the MEWMA with the normal-theory limits in terms of the in-control average run lengths. An extension study of the two-sided MPEWMA to a one-sided version is performed; this is useful for detecting an increase in the count means. The results of comparison with the one-sided MEWMA chart are quite similar to the two-sided case. The implementation of the MPEWMA scheme for multiple count data is illustrated, with step by step guidelines and several examples. In addition, the method is compared to other model-based control charts that are used to monitor the residual values such as the regression adjustment. The MPEWMA scheme shows better performance on detecting the mean shift in count data when positive correlation exists among all variables. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

Computer integrated manufacturing environments and competition among companies to meet customer requirements raise the need for the use of online methodologies in combination with traditional Statistical Process Control tools. This study focuses on detecting the change point, when a shift in mean occurs, in a normal bivariate process using two different approaches. First, Multivariate Cumulative Sum (MCUSUM) and Multivariate Exponentially Weighted Moving Average (MEWMA) statistical procedures were used in detecting the mean shift in the process. Then the step-change detection and neural network approaches were applied to the outputs of MCUSUM and MEWMA statistical procedures to identify the time of the change. The results show that the step-change and neural network approaches are capable of detecting the time of the change earlier than either the MCUSUM or MEWMA statistical procedure.

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.

O combate ao roubo de veículos requer monitoramento constante e ações policiais para alterar a logística de rondas. A proposta deste trabalho é apresentar uma aplicação de como monitorar o índice de roubo de veículos nos 93 distritos da cidade de São Paulo e estabelecer alertas quando houver um aumento da criminalidade que é considerado fora do padrão histórico. Para modelar a taxa de roubo em todos os distritos da cidade foi utilizado o modelo STARMA (Spatio-Time Autoregressive Moving Average) que incorpora dependência espaço-temporal. Já para os gráficos de controle foram utilizados o MEWMA (Multivariate Exponentially Weighted Moving Average) e o MCUSUM (Multivariate Cumulative Sum) direcionado para capturar aumentos. Os resultados indicaram que o MCUSUM teve um tempo de reação a aumentos da criminalidade menor que o MEWMA. Além disso, foi testado como seria o tempo de reação dessas estatísticas sem a presença da componente espacial do modelo STARMA e o resultado foi uma reação incorreta, com aumento de falsos positivos. Palavras-chaves: logística, gráficos de controle, STARMA, MCUSUM, MEWMA. / A constant monitoring and police actions to change the routes of patrol vehicles are some requirements to act against the vehicle theft. The purpose of this dissertation is to present an application of monitoring the vehicle theft rates by control charts in the 93 police districts of the city of SãoPaulo. The control charts are built to detect increases in the crime rates, so a signal is triggered in regions where the crime rates are considered abnormal from the historical pattern. A STARMA (Spatio-Time Autoregressive Moving Average) model that incorporates space-time dependency is used to model the rate of robbery in all districts. MEWMA (Multivariate Exponentially Weighted Moving Average) and the MCUSUM (Multivariate Cumulative Sum) are built to meet some performance criteria. The results pointed out that MCUSUM outperforms MEWMA to capture increases in crime. Additionally earlier false alarms are observed in both charts as consequences when spatial components of STARMA model are wrongly omitted.

abstract: The emergence of new technologies as well as a fresh look at analyzing existing processes have given rise to a new type of response characteristic, known as a profile. Profiles are useful when a quality variable is functionally dependent on one or more explanatory, or independent, variables. So, instead of observing a single measurement on each unit or product a set of values is obtained over a range which, when plotted, takes the shape of a curve. Traditional multivariate monitoring schemes are inadequate for monitoring profiles due to high dimensionality and poor use of the information stored in functional form leading to very large variance-covariance matrices. Profile monitoring has become an important area of study in statistical process control and is being actively addressed by researchers across the globe. This research explores the understanding of the area in three parts. A comparative analysis is conducted of two linear profile-monitoring techniques based on probability of false alarm rate and average run length (ARL) under shifts in the model parameters. The two techniques studied are control chart based on classical calibration statistic and a control chart based on the parameters of a linear model. The research demonstrates that a profile characterized by a parametric model is more efficient monitoring scheme than one based on monitoring only the individual features of the profile. A likelihood ratio based changepoint control chart is proposed for detecting a sustained step shift in low order polynomial profiles. The test statistic is plotted on a Shewhart like chart with control limits derived from asymptotic distribution theory. The statistic is factored to reflect the variation due to the parameters in to aid in interpreting an out of control signal. The research also looks at the robust parameter design study of profiles, also referred to as signal response systems. Such experiments are often necessary for understanding and reducing the common cause variation in systems. A split-plot approach is proposed to analyze the profiles. It is demonstrated that an explicit modeling of variance components using generalized linear mixed models approach has more precise point estimates and tighter confidence intervals. / Dissertation/Thesis / Ph.D. Industrial Engineering 2010

O combate ao roubo de veículos requer monitoramento constante e ações policiais para alterar a logística de rondas. A proposta deste trabalho é apresentar uma aplicação de como monitorar o índice de roubo de veículos nos 93 distritos da cidade de São Paulo e estabelecer alertas quando houver um aumento da criminalidade que é considerado fora do padrão histórico. Para modelar a taxa de roubo em todos os distritos da cidade foi utilizado o modelo STARMA (Spatio-Time Autoregressive Moving Average) que incorpora dependência espaço-temporal. Já para os gráficos de controle foram utilizados o MEWMA (Multivariate Exponentially Weighted Moving Average) e o MCUSUM (Multivariate Cumulative Sum) direcionado para capturar aumentos. Os resultados indicaram que o MCUSUM teve um tempo de reação a aumentos da criminalidade menor que o MEWMA. Além disso, foi testado como seria o tempo de reação dessas estatísticas sem a presença da componente espacial do modelo STARMA e o resultado foi uma reação incorreta, com aumento de falsos positivos. Palavras-chaves: logística, gráficos de controle, STARMA, MCUSUM, MEWMA. / A constant monitoring and police actions to change the routes of patrol vehicles are some requirements to act against the vehicle theft. The purpose of this dissertation is to present an application of monitoring the vehicle theft rates by control charts in the 93 police districts of the city of SãoPaulo. The control charts are built to detect increases in the crime rates, so a signal is triggered in regions where the crime rates are considered abnormal from the historical pattern. A STARMA (Spatio-Time Autoregressive Moving Average) model that incorporates space-time dependency is used to model the rate of robbery in all districts. MEWMA (Multivariate Exponentially Weighted Moving Average) and the MCUSUM (Multivariate Cumulative Sum) are built to meet some performance criteria. The results pointed out that MCUSUM outperforms MEWMA to capture increases in crime. Additionally earlier false alarms are observed in both charts as consequences when spatial components of STARMA model are wrongly omitted.

Multivariate control charts are used to monitor a process when more than one quality variable associated with the process is being observed. The multivariate exponentially weighted moving average (MEWMA) control chart is one of the most commonly recommended tools for multivariate process monitoring. The standard practice, when using the MEWMA control chart, is to take samples of fixed size at regular sampling intervals for each variable. In the first part of this dissertation, MEWMA control charts based on sequential sampling schemes with two possible stages are investigated. When sequential sampling with two possible stages is used, observations at a sampling point are taken in two groups, and the number of groups actually taken is a random variable that depends on the data. The basic idea is that sampling starts with a small initial group of observations, and no additional sampling is done at this point if there is no indication of a problem with the process. But if there is some indication of a problem with the process then an additional group of observations is taken at this sampling point. The performance of the sequential sampling (SS) MEWMA control chart is compared to the performance of standard control charts. It is shown that that the SS MEWMA chart is substantially more efficient in detecting changes in the process mean vector than standard control charts that do not use sequential sampling. Also the situation is considered where different variables may have different measurement costs. MEWMA control charts with unequal sample sizes based on differing measurement costs are investigated in order to improve the performance of process monitoring. Sequential sampling plans are applied to MEWMA control charts with unequal sample sizes and compared to the standard MEWMA control charts with a fixed sample size. The steady-state average time to signal (SSATS) is computed using simulation and compared for some selected sets of sample sizes. When different variables have significantly different measurement costs, using unequal sample sizes can be more cost effective than using the same fixed sample size for each variable. In the second part of this dissertation, control chart methods are proposed for process monitoring when the quality of a process or product is characterized by a linear function. In the historical analysis of Phase I data, methods including the use of a bivariate <i>T</i>² chart to check for stability of the regression coefficients in conjunction with a univariate Shewhart chart to check for stability of the variation about the regression line are recommended. The use of three univariate control charts in Phase II is recommended. These three charts are used to monitor the <i>Y</i>-intercept, the slope, and the variance of the deviations about the regression line, respectively. A simulation study shows that this type of Phase II method can detect sustained shifts in the parameters better than competing methods in terms of average run length (ARL) performance. The monitoring of linear profiles is also related to the control charting of regression-adjusted variables and other methods. / Ph. D.