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.

When a reliability experiment is used, practitioners can understand better what lifetimes to expect of a product under different operating conditions and what factors are important to designing reliability into a product. Reliability experiments, however, can be very challenging to analyze because often the reliability or lifetime data tend to follow distinctly non-normal distributions and the experiments typically involve censoring. Time and cost constraints may also lead to reliability experiments with experimental protocols that are not completely randomized. In many industrial experiments, for example, the split-plot structure arises when the randomization of the experimental runs is restricted. Additionally, for many reliability experiments, it is often cost effective to apply a treatment combination to a stand with multiple units on it as opposed to each unit individually, which introduces subsampling. The analysis of lifetime data assuming a completely randomized design has been well studied, but until recently analysis methodologies for more complex experimental designs with multiple error terms have not been a focus of the reliability field. This dissertation provides two analysis methods for analyzing right-censored Weibull distributed lifetime data from a split-plot experiment with subsampling. We evaluate the proposed methods through a simulation study. Companies also routinely perform life tests on their products to ensure that products meet requirements. Each of these life tests typically involves testing several units simultaneously with interest in the times to failure. Again, the fact that lifetime data tend to be nonnormally distributed and censored make the development of a control charting procedure more demanding. In this dissertation, one-sided lower and upper likelihood ratio based cumulative sum (CUSUM) control charting procedures are developed for right-censored Weibull lifetime data to monitor changes in the scale parameter, also known as the characteristic life, for a fixed value of the Weibull shape parameter. Because a decrease in the characteristic life indicates a decrease in the mean lifetime of a product, a one-sided lower CUSUM chart is the main focus. We illustrate the development and implementation of the chart and evaluate the properties through a simulation study. / Ph. D.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

Neste trabalho propomos gráficos de controle tipo CUSUM para monitoramento de tempos de sobrevivência. Nossa proposta é desenvolver diferentes estatísticas para o escore do gráfico CUSUM de forma prospectiva. Inicialmente propomos um gráfico CUSUM não paramétrico para monitoramento de populações homogêneas que avalia a variação na estatística log-rank como forma de identificar se há uma mudança significativa no risco de falha ao longo do tempo. Algumas abordagens diferentes foram consideradas e em destaque colocamos o gráfico ZDiff CUSUM, que tem como escore o incremento na estatística Z do teste log-rank em relação à inspeção anterior. Foi constatado, via simulação, que este método é eficiente. Posteriormente investigamos abordagens que levam em conta heterogeneidade na população por meio do modelo de Cox, considerando medidas baseadas na razão de verossimilhanças e em resíduos martingal e deviance. Através de simulações, verificou-se que o método com base na razão de verossimilhanças se mostrou ágil para detectar alteração na taxa de falha, quando se conhece a intensidade da mudança e este valor é informado na construção do teste. Por outro lado, os gráficos CUSUM com base em resíduos são mais simples e se mostraram eficazes para identificar aumentos no padrão da sobrevivência. Estes três métodos e o ZDiff CUSUM foram aplicados a dados de um estudo conduzido no Instituto do Coração (InCor) envolvendo pacientes com insuficiência cardíaca. Foi detectado que ao longo do tempo estes pacientes apresentam sobrevida maior, o que pode estar ligado à melhoria no tratamento e procedimentos realizados no hospital. Como conclusão, sugerimos que os gráficos tipo CUSUM com resíduos do modelo de Cox e o método não paramétrico com teste log-rank podem ser alternativas para utilização na prática em monitoramento de dados de sobrevivência. / In this work we propose CUSUM control charts to monitor survival times. Our proposal is to develop different statistics for the CUSUM chart score in a prospective way, to take into account SA approaches. We initially consider a non-parametric approach to monitor homogeneous populations. This CUSUM evaluates the variation on the log-rank test statistics as a way to identify significant changes in the risk of failure. Some different expressions for this have been considered and, in particular, we propose a ZDiff CUSUM chart computed as the increment on the log-rank test statistics Z at each inspection point in relation to the previous one. Based on simulation studies it was found that this method is efficient. Subsequently we investigated approaches that take into account heterogeneity in the population through the Cox model, considering measures based on the likelihood ratio and on martingal and deviance residuals. Through simulations, it was verified that the method based on the likelihood ratio was agile to detect a change in the hazard rate, when the intensity of the change is known and this value is informed in the construction of the test. On the other hand, CUSUM methods based on residuals are simpler and have been shown to be effective in identifying increases in survival pattern. These three methods and the ZDiff CUSUM were applied to a dataset from a study conducted at the Heart Institute (InCor) on patients with heart failure. It has been found that, over time, these patients have greater survival, which may be linked to improved treatment and procedures performed at the hospital. As a conclusion, we suggest that the CUSUM methods based on Cox model residuals and the nonparametric method on the log-rank test may be alternatives for practice in monitoring survival data.

In spite of the remarkable development of modern medical treatment and technology, the threat of pandemic diseases such as anthrax, cholera, and SARS has not disappeared. As a part of emerging healthcare decision problems, many researchers have studied how to detect and contain disease outbreaks, and our research is aligned with this trend. This thesis mainly consists of two parts: epidemic simulation modeling for effective intervention strategies and spatiotemporal monitoring for outbreak detection. We developed a stochastic epidemic simulation model of a pandemic influenza virus (H1N1) to test possible interventions within a structured population. The possible interventions — such as vaccination, antiviral treatment, household prophylaxis, school closure and social distancing — are investigated in a large number of scenarios, including delays in vaccine delivery and low and moderate efficacy of the vaccine. Since timely and accurate detection of a disease outbreak is crucial in terms of preparation for emergencies in healthcare and biosurveillance, we suggest two spatiotemporal monitoring charts, namely, the SMCUSUM and RMCUSUM charts, to detect increases in the rate or count of disease incidents. Our research includes convenient methods to approximate the control limits of the charts. An analytical control limit approximation method for the SMCUSUM chart performs well under certain conditions on the data distribution and monitoring range. Another control limit approximation method for the RMCUSUM chart provides robust performance to various monitoring range, spatial correlation structures, and data distributions without intensive modeling of the underlying process.

Generalized likelihood ratio (GLR) control charts are investigated for two types of statistical process monitoring (SPC) problems. The first part of this dissertation considers the problem of monitoring a normally distributed process variable when a special cause may produce a time varying linear drift in the mean. The design and application of a GLR control chart for drift detection is investigated. The GLR drift chart does not require specification of any tuning parameters by the practitioner, and has the advantage that, at the time of the signal, estimates of both the change point and the drift rate are immediately available. An equation is provided to accurately approximate the control limit. The performance of the GLR drift chart is compared to other control charts such as a standard CUSUM chart and a CUSCORE chart designed for drift detection. We also compare the GLR chart designed for drift detection to the GLR chart designed for sustained shift detection since both of them require only a control limit to be specified. In terms of the expected time for detection and in terms of the bias and mean squared error of the change-point estimators, the GLR drift chart has better performance for a wide range of drift rates relative to the GLR shift chart when the out-of-control process is truly a linear drift. The second part of the dissertation considers the problem of monitoring a linear functional relationship between a response variable and one or more explanatory variables (a linear profile). The design and application of GLR control charts for this problem are investigated. The likelihood ratio test of the GLR chart is generalized over the regression coefficients, the variance of the error term, and the possible change-point. The performance of the GLR chart is compared to various existing control charts. We show that the overall performance of the GLR chart is much better than other options in detecting a wide range of shift sizes. The existing control charts designed for certain shifts that may be of particular interest have several chart parameters that need to be specified by the user, which makes the design of such control charts more difficult. The GLR chart is very simple to design, as it is invariant to the choice of design matrix and the values of in-control parameters. Therefore there is only one design parameter (the control limit) that needs to be specified. Especially, the GLR chart can be constructed based on the sample size of n=1 at each sampling point, whereas other charts cannot be applied. Another advantage of the GLR chart is its built-in diagnostic aids that provide estimates of both the change-point and the values of linear profile parameters. / Ph. D.

The generalized likelihood ratio (GLR) control charts are studied for monitoring a process proportion of defective or nonconforming items. The type of process change considered is an abrupt sustained increase in the process proportion, which implies deterioration of the process quality. The objective is to effectively detect a wide range of shift sizes. For the first part of this research, we assume samples are collected using rational subgrouping with sample size n>1, and the binomial GLR statistic is constructed based on a moving window of past sample statistics that follow a binomial distribution. Steady state performance is evaluated for the binomial GLR chart and the other widely used binomial charts. We find that in terms of the overall performance, the binomial GLR chart is at least as good as the other charts. In addition, since it has only two charting parameters that both can be easily obtained based on the approach we propose, less effort is required to design the binomial GLR chart for practical applications. The second part of this research develops a Bernoulli GLR chart to monitor processes based on the continuous inspection, in which case samples of size n=1 are observed. A constant upper bound is imposed on the estimate of the process shift, preventing the corresponding Bernoulli GLR statistic from being undefined. Performance comparisons between the Bernoulli GLR chart and the other charts show that the Bernoulli GLR chart has better overall performance than its competitors, especially for detecting small shifts. / Ph. D.

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.

When monitoring a binary process proportion p, it is usually assumed that the binary observations are independent. However, it is very common that the observations are correlated with p being the correlation between two successive observations. The first part of this research investigates the problem of monitoring p when the binary observations follow a first-order two-state Markov chain model with p remaining unchanged. A Markov Binary GLR (MBGLR) chart with an upper bound on the estimate of p is proposed to monitor a continuous stream of autocorrelated binary observations treating each observation as a sample of size n=1. The MBGLR chart with a large upper bound has good overall performance over a wide range of shifts. The MBGLR chart is optimized using the extra number of defectives (END) over a range of upper bounds for the MLE of p. The numerical results show that the optimized MBGLR chart has a smaller END than the optimized Markov binary CUSUM. The second part of this research develops a CUSUM-pp chart and a GLR-pp chart to monitor p and p simultaneously. The CUSUM-pp with two tuning parameters is designed to detect shifts in p and p when the shifted values are known. We apply two CUSUM-pp charts as a chart combination to detect increases in p and increases or decreases in p. The GLR-pp chart with an upper bound on the estimate of p, and an upper bound and a lower bound on the estimate of p works well when the shifts are unknown. We find that the GLR-pp chart has better overall performance. The last part of this research investigates the problem of monitoring p with p remains at the target value when the correlated binary observations are aggregated into samples with n>1. We assume that samples are independent and there is correlation between the observations in a sample. We proposed some GLR and CUSUM charts to monitor p and the performance of the charts are compared. The simulation results show MBNGLR has overall better performance than the other charts. / Ph. D.