Even a modest positive autocorrelation results in a considerable increase in the number of false alarms that are produced when applying a CUSUM chart. Knowledge of the process to be controlled allows for suitable adaptation of the CUSUM procedure. If one has to suspect the normality assumption, nonparametric control procedures such as the rank-based CUSUM chart are a practical alternative. The paper reports the results of a simulation study on the robustness (in terms of sensitivity of the ARL) of the rank-based CUSUM chart against serial correlation of the control variable. The results indicate that the rank-based CUSUM chart is less affected by correlation than the observation-based chart: The rank-based CUSUM chart shows a smaller increase in the number of false alarms and a higher decrease in the ARL in the out-of-control case than the the observation-based chart. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

No description available.

The risk-adjusted Bernoulli cumulative sum (CUSUM) chart developed by Steiner et al. (2000) is an increasingly popular tool for monitoring clinical and surgical performance. In practice, however, use of a fixed control limit for the chart leads to quite variable in-control average run length (ARL) performance for patient populations with different risk score distributions. To overcome this problem, the simulation-based dynamic probability control limits (DPCLs) patient-by-patient for the risk-adjusted Bernoulli CUSUM charts is determined in this study. By maintaining the probability of a false alarm at a constant level conditional on no false alarm for previous observations, the risk-adjusted CUSUM charts with DPCLs have consistent in-control performance at the desired level with approximately geometrically distributed run lengths. Simulation results demonstrate that the proposed method does not rely on any information or assumptions about the patients' risk distributions. The use of DPCLs for risk-adjusted Bernoulli CUSUM charts allows each chart to be designed for the corresponding particular sequence of patients for a surgeon or hospital. The effect of estimation error on performance of risk-adjusted Bernoulli CUSUM chart with DPCLs is also examined. Our simulation results show that the in-control performance of risk-adjusted Bernoulli CUSUM chart with DPCLs is affected by the estimation error. The most influential factors are the specified desired in-control average run length, the Phase I sample size and the overall adverse event rate. However, the effect of estimation error is uniformly smaller for the risk-adjusted Bernoulli CUSUM chart with DPCLs than for the corresponding chart with a constant control limit under various realistic scenarios. In addition, there is a substantial reduction in the standard deviation of the in-control run length when DPCLs are used. Therefore, use of DPCLs has yet another advantage when designing a risk-adjusted Bernoulli CUSUM chart. These researches are results of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech). Moreover, DPCLs are adapted to design the risk-adjusted CUSUM charts for multiresponses developed by Tang et al. (2015). It is shown that the in-control performance of the charts with DPCLs can be controlled for different patient populations because these limits are determined for each specific sequence of patients. Thus, the risk-adjusted CUSUM chart for multiresponses with DPCLs is more practical and should be applied to effectively monitor surgical performance by hospitals and healthcare practitioners. This research is a result of joint work with Dr. William H. Woodall (Department of Statistics, Virginia Tech) and Mr. Justin Loda (Department of Statistics, Virginia Tech). / Ph. D.

[EN] The Statistical Process Control (SPC) is a method used to control the quality characteristics of a product during the production process, determine whether the manufacturing process is or not stable and improve its capacity through the reduction of variability. One of the main tools used in the SPC is the control chart. Often the quality of a product is measured through various quality characteristics generally correlated. Multivariate Control charts are a response to the need for quality control in such situations. If the quality characteristics are qualitative, sometimes it happens that the product quality is defined by linguistic variables and product units are also classified by linguistic forms into several categories, depending on the degree of fulfillment of expectations, creating a situation of fuzzy classifications. The control charts proposed in the literature to deal with such situations are mostly based on simulation and using approximation techniques which hinder the practical application thereof. This thesis addresses this issue proposing a multivariate control chart for quality characteristics of multi-type attributes correlated based on the T2 control chart of Hotelling, using a fuzzy approach. The results of the proposed control charts before are improved by establishing a more formal way of measuring and evaluating quality in these diffuse situations. A method is also proposed to assess the performance of control chart proposed, by deter mining the average run length (ARL), in both in-control state and the out-of-control state. For this, algorithms which use Monte Carlo simulation are developed and implemented in R. Additionally, the sensitivity of the control chart faced with the choice of the membership functions of linguistic variables is analyzed. / [ES] El Control Estadístico de Procesos (CEP) es un método que se utiliza para controlar las características de calidad de un producto durante el proceso de producción, determinar si los procesos de manufactura son o no estables y mejorar su capacidad a través de la reducción de la variabilidad. Una de las principales herramientas utilizadas en el Control Estadístico de Procesos es el gráfico de control. Con frecuencia, la calidad de un producto se mide a través de varias características de calidad, generalmente correlacionadas. Los gráficos de control multivariantes son una respuesta a la necesidad de controlar la calidad en tales situaciones. Si las características de calidad son de carácter cualitativo, ocurre en ocasiones que la calidad del producto se define mediante variables lingüísticas y las unidades de producto se clasifican también de for ma lingüística en varias categorías, dependiendo del grado de cumplimiento de las expectativas, creando una situación de clasificaciones difusas. Los gráficos propuestos en la literatura para tratar con tales situaciones están, en su mayoría, basados en simulación y el uso de técnicas de aproximación que dificultan la aplicación práctica de los mismos. Esta tesis trata esta cuestión proponiendo un Gráfico de Control multivariante para características de calidad de tipo multi-atributos correlacionados basado en el gráfico T2 de Hotelling, utilizando un enfoque difuso. Se mejora los resultados de los gráficos de control propuestos anterior mente estableciendo una manera más formal de medición y evaluación de la calidad en estas situaciones difusas. Se propone además un procedimiento para evaluar el rendimiento del gráfico de control propuesto mediante la determinación de la longitud de racha promedio (ARL), tanto para un estado bajo-control como para el estado fuera-de-control. Para ello se desarrollaron algoritmos que utilizan simulación de Monte Carlo y han sido implementados en R. Adicionalmente, se analiza la sensibilidad del gráfico de control frente a la elección de las funciones de pertenencia de las variables lingüísticas. / [CA] El Control Estadístic de Processos (CEP) és un mètode que s'utilitza per controlar les característiques de qualitat d'un producte durant el procés de producció, deter minar si els processos de manufactura són o no estables i millorar la seva capacitat a través de la reducció de la variabilitat. Una de les principals eines utilitzades en el Control Estadístic de Processos és el gràfic de control. Sovint, la qualitat d'un producte es mesura a través de diverses característiques de qualitat, generalment correlacionades. Els gràfics de control multivariants són una resposta a la necessitat de controlar la qualitat en aquestes situacions. Si les característiques de qualitat són de caràcter qualitatiu, de vegades passa que la qualitat del producte es defineix mitjançant variables lingüístiques i les unitats de producte es classifiquen també de for ma lingüística en diverses categories, depenent del grau de compliment de les expectatives, creant una situació de classificacions difuses. Els gràfics proposats en la literatura per abordar aquestes situacions són, majoritàriament, basats en simulació i l'ús de tècniques d'aproximació que en dificulten l'aplicació pràctica. Aquesta tesi tracta de resoldre aquesta qüestió amb la proposta d'un Gràfic de Control multivariant per característiques de qualitat de tipus multi-atributs correlacionats basat en el gràfic T2 de Hotelling, mijançant un enfocament difús. S'hi milloren els resultats de les gràfics de control proposats anterior ment per mitjà d'un mètode més for mal de mesurament i avaluació de la qualitat en aquestes situacions difuses. S'hi proposa a més un procediment per avaluar el rendiment del gràfic de control proposat mitjançant la deter minació de la longitud de ràfega mitjana (ARL), tant per a un estat en-control com per a l'estat fora-de-control. Amb aquesta finalitat es van desenvolupar algoritmes que utilitzen simulació de Monte Carlo i han estat implementats en R. Addicionalment, s'hi analitza la sensibilitat del gràfic de control davant l'elecció de les funcions de pertinença de les variables lingüístiques. / Pastuizaca Fernández, MN. (2016). Diseño y mejora de gráficos de control multivariantes para atributos. Un enfoque basado en teoría difusa [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/65073

Statistical Process Control (SPC), and in particular control charting, is widely used to achieve and maintain control of various processes in manufacturing. A control chart is a graphical display that plots quality characteristics versus the sample number or the time line. Interest in effective implementation of control charts for autocorrelated processes has increased in recent years. However, because of the complexities involved, few systematic design approaches have thus far been developed. Many control charting methods can be viewed as the charting of the output of a linear filter applied to the process data. In this dissertation, we generalize the concept of linear filters for control charts and propose new control charting schemes, the general linear filter (GLF) and the 2nd-order linear filter, based on the generalization. In addition, their optimal design methodologies are developed, where the filter parameters are optimally selected to minimize the out-of-control Average Run Length (ARL) while constraining the in-control ARL to some desired value. The optimal linear filters are compared with other methods in terms of ARL performance, and a number of their interesting characteristics are discussed for various types of mean shifts (step, spike, sinusoidal) and various ARMA process models (i.i.d., AR(1), ARMA(1,1)). Also, in this work, a new discretization approach for substantially reducing the computational time and memory use for the Markov chain method of calculating the ARL is proposed. Finally, a gradient-based optimization strategy for searching optimal linear filters is illustrated.

In epidemiology it is often useful to monitor disease occurrences prospectively to determine the location and time when clusters of disease are forming. This aids in the prevention of illness and injury of the public and is the reason spatio-temporal disease surveillance methods are implemented. Care must be taken in the design and implementation of these types of surveillance methods so that the methods provide accurate information on the development of clusters. Here two spatio-temporal methods for prospective disease surveillance are considered. These include the local Knox monitoring method and a new wavelet-based prospective monitoring method. The local Knox surveillance method uses a cumulative sum (CUSUM) control chart for monitoring the local Knox statistic, which tests for space-time clustering each time there is an incoming observation. The detection of clusters of events occurring close together both temporally and spatially is important in finding outbreaks of disease within a specified geographic region. The local Knox surveillance method is based on the Knox statistic, which is often used in epidemiology to test for space-time clustering retrospectively. In this method, a local Knox statistic is developed for use with the CUSUM chart for prospective monitoring so that epidemics can be detected more quickly. The design of the CUSUM chart used in this method is considered by determining the in-control average run length (ARL) performance for different space and time closeness thresholds as well as for different control limit values. The effect of nonuniform population density and region shape on the in-control ARL is explained and some issues that should be considered when implementing this method are also discussed. In the wavelet-based prospective monitoring method, a surface of incidence counts is modeled over time in the geographical region of interest. This surface is modeled using Poisson regression where the regressors are wavelet functions from the Haar wavelet basis. The surface is estimated each time new incidence data is obtained using both past and current observations, weighing current observations more heavily. The flexibility of this method allows for the detection of changes in the incidence surface, increases in the overall mean incidence count, and clusters of disease occurrences within individual areas of the region, through the use of control charts. This method is also able to incorporate information on population size and other covariates as they change in the geographical region over time. The control charts developed for use in this method are evaluated based on their in-control and out-of-control ARL performance and recommendations on the most appropriate control chart to use for different monitoring scenarios is provided. / Ph. D.

Ce mémoire a pour objectif de déterminer si les précipitations convectives estivales simulées par le modèle régional canadien du climat (MRCC) sont stationnaires ou non à travers le temps. Pour répondre à cette question, nous proposons une méthodologie statistique de type fréquentiste et une de type bayésien. Pour l'approche fréquentiste, nous avons utilisé le contrôle de qualité standard ainsi que le CUSUM afin de déterminer si la moyenne a augmenté à travers les années. Pour l'approche bayésienne, nous avons comparé la distribution a posteriori des précipitations dans le temps. Pour ce faire, nous avons modélisé la densité \emph{a posteriori} d'une période donnée et nous l'avons comparée à la densité a posteriori d'une autre période plus éloignée dans le temps. Pour faire la comparaison, nous avons utilisé une statistique basée sur la distance d'Hellinger, la J-divergence ainsi que la norme L2. Au cours de ce mémoire, nous avons utilisé l'ARL (longueur moyenne de la séquence) pour calibrer et pour comparer chacun de nos outils. Une grande partie de ce mémoire sera donc dédiée à l'étude de l'ARL. Une fois nos outils bien calibrés, nous avons utilisé les simulations pour les comparer. Finalement, nous avons analysé les données du MRCC pour déterminer si elles sont stationnaires ou non. / The main goal of this master's thesis is to find whether the summer convective precipitations simulated by the Canadian Regional Climate Model (CRCM) are stationary over time or not. In order to answer that question, we propose both a frequentist and Bayesian statistical methodology. For the frequentist approach, we used standard quality control and the CUSUM to determine if the mean has increased over the years. For the Bayesian approach, we compared the posterior distributions of the precipitations over time. In order to do the comparison, we used a statistic based on the Hellinger's distance, the J-divergence and the L2 norm. In this master's thesis, we used the ARL (average run length) to calibrate each of our methods. Therefore, a big part of this thesis is about studying the actual property of the ARL. Once our tools are well calibrated, we used the simulation to compare them together. Finally, we studied the data from the CRCM to decide, whether or not, the data are stationary.

The Atlantic Forest of south-eastern Brazil is a hot-spot for biodiversity and should be conserved. It is also at the center of the largest municipalities in Brazil and therefore has a severely fragmented landscape. Iracambi, a working farm near the Serra do Brigadeiro state park in Minas Gerais, is working for conservation in an area of intense agricultural production and expanding forestry industry. Most households in this rural area have some amount of eucalyptus on their property and consequently the director of Iracambi is developing the preliminary foundation for a forest corridor program comprised of primarily eucalyptus with the goal of integrating native species whenever possible. In this research, an exploratory case study was conducted with the purpose of determining if an integrated forest corridor should be considered as a viable option for Iracambi in the greater Serra do Brigadeiro region (near the communities of Araponga, Ervália, Fervadouro, Miradouro, Pedra Bonita, and Sericita). The majority of the survey participants revealed interest in the proposed forest corridor program and many expressed further interest if this would help them achieve compliance with the environmental law requiring a Legal Reserve Area (ARL) on private property. There is a need and a desire for programs that would subsidize ARL adherence in this area, since many studies recognize that adherence levels are at approximately ten percent nationally. Barriers to implementation, however, include cultural barriers that would primarily require acceptance with influential community members, knowledge and cost barriers associated with proper stand management, and current economic circumstances which lack a market for sustainably produced, higher quality eucalyptus timber. Additionally, policy barriers, which do not provide sufficient incentives to comply with environmental laws, further impede implementation of an integrated forest corridor program in this area. If these key barriers to implementation could be addressed, an integrated forest corridor program could prove as a viable option for Iracambi and this area and therefore, this thesis offers some recommendations for the successful implementation of this proposed program.

Ce mémoire a pour objectif de déterminer si les précipitations convectives estivales simulées par le modèle régional canadien du climat (MRCC) sont stationnaires ou non à travers le temps. Pour répondre à cette question, nous proposons une méthodologie statistique de type fréquentiste et une de type bayésien. Pour l'approche fréquentiste, nous avons utilisé le contrôle de qualité standard ainsi que le CUSUM afin de déterminer si la moyenne a augmenté à travers les années. Pour l'approche bayésienne, nous avons comparé la distribution a posteriori des précipitations dans le temps. Pour ce faire, nous avons modélisé la densité \emph{a posteriori} d'une période donnée et nous l'avons comparée à la densité a posteriori d'une autre période plus éloignée dans le temps. Pour faire la comparaison, nous avons utilisé une statistique basée sur la distance d'Hellinger, la J-divergence ainsi que la norme L2. Au cours de ce mémoire, nous avons utilisé l'ARL (longueur moyenne de la séquence) pour calibrer et pour comparer chacun de nos outils. Une grande partie de ce mémoire sera donc dédiée à l'étude de l'ARL. Une fois nos outils bien calibrés, nous avons utilisé les simulations pour les comparer. Finalement, nous avons analysé les données du MRCC pour déterminer si elles sont stationnaires ou non. / The main goal of this master's thesis is to find whether the summer convective precipitations simulated by the Canadian Regional Climate Model (CRCM) are stationary over time or not. In order to answer that question, we propose both a frequentist and Bayesian statistical methodology. For the frequentist approach, we used standard quality control and the CUSUM to determine if the mean has increased over the years. For the Bayesian approach, we compared the posterior distributions of the precipitations over time. In order to do the comparison, we used a statistic based on the Hellinger's distance, the J-divergence and the L2 norm. In this master's thesis, we used the ARL (average run length) to calibrate each of our methods. Therefore, a big part of this thesis is about studying the actual property of the ARL. Once our tools are well calibrated, we used the simulation to compare them together. Finally, we studied the data from the CRCM to decide, whether or not, the data are stationary.

No description available.