452 research outputs found
A semi-empirical Bayesian chart to monitor Weibull percentiles
This paper develops a Bayesian control chart for the percentiles of the
Weibull distribution, when both its in-control and out-of-control parameters
are unknown. The Bayesian approach enhances parameter estimates for small
sample sizes that occur when monitoring rare events as in high-reliability
applications or genetic mutations. The chart monitors the parameters of the
Weibull distribution directly, instead of transforming the data as most
Weibull-based charts do in order to comply with their normality assumption. The
chart uses the whole accumulated knowledge resulting from the likelihood of the
current sample combined with the information given by both the initial prior
knowledge and all the past samples. The chart is adapting since its control
limits change (e.g. narrow) during the Phase I. An example is presented and
good Average Run Length properties are demonstrated. In addition, the paper
gives insights into the nature of monitoring Weibull processes by highlighting
the relationship between distribution and process parameters.Comment: 21 pages, 3 figures, 5 table
Monitoring regression models for lifetimes
Abstract. Monitoring regression models for lifetimes The current study addresses the monitoring of regression models with response variable having a distribution for lifetimes. Certain aspects of this research have relevant importance. First of all, in most of the existing literature, monitoring regression models is treated as a special case of profile monitoring. However, especially in some industrial and healthcare applications, regression models can adequately represent process quality but cannot always be qualified as profiles. This is the case of regression models for lifetimes. The fact is that lifetimes can be measured just once at most in the same experimental unit. Consequently, the nature of responses while monitoring regression models is not multivariate necessarily. However, the main goal of monitoring regression models for lifetimes aims to check the stability of the distributions of n response variables Yi , i = 1, · · · , n. As all these distributions are linked by the same parameter vector, the stability of the formers depends on the one of the latter. Thus, it is clear that profile monitoring and regression monitoring share the same purpose. Techniques from profile monitoring can be used for successfully monitoring regression models for lifetimes as well. Some methodologies for monitoring Weibull regression models for lifetimes with common shape parameter and in phase II processes will be addressed depending on the composition of available regression data structures. The monitoring of the parameter vector characterizing the Weibull regression model allows us to make conclusions about the mean value of the response variable. It will be shown that the monitoring of regression models for lifetimes can be carried out by redesigning existing methods from monitoring continuous quality variables and profile monitoring. In the presence of uncensored lifetimes, it was found out that it is possible to adapt conventional control charts for single observations to the monitoring of the common shape parameter. It is also possible to adapt control techniques and methodologies from profile monitoring to the case of monitoring the entire parameter vector characterizing the basic model. In both cases, chart designing depends on the asymptotic normality of the maximum likelihood estimator of the parameter vector. Thus, it is necessary to implement some existing corrections to the monitoring statistics so that existing control charts work acceptably well when non-large enough data sets are available. When a type I right-censored mechanism is operating on lifetimes, the monitoring can be carried out with the help of one-sided likelihood ratio based cumulative sum control charts. Theese procedures can be used for monitoring one or more of the parameters in the parameter vector and has practically no restrictions respect to the dataset dimension needed for monitoring. Conducted simulations suggest that this chart is more effective than the multivariate exponentially weighted moving average method when detecting the deterioration of the process is wanted.Monitoreo de modelos de regresión para tiempos de vida El presente estudio se aborda el monitoreo de modelos de regresión para tiempos de vida. Ciertos aspectos de este trabajo son de crucial importancia. Como primera medida, en gran parte de la literatura especializada, el monitoreo de modelos de regresión se trata como un caso particular del monitoreo de perfiles. Sin embargo, existen muchas aplicaciones, especialmente en ingenierÃa y en cuidados en salud, en las cuales los modelos de regresión pueden caracterizar adecuadamente la calidad de los procesos pero no siempre pueden considerarse como perfiles. Es el caso de los modelos de regresión para tiempos de vida. El hecho es que, en general, un tiempo de vida puede medirse a lo sumo una vez en la misma unidad experimental. Consecuentemente, la naturaleza de las respuestas en el monitoreo de modelos de regresión no necesariamente es multivariada. Sin embargo, el objetivo principal del montireo de modelos regresión apunta a verificar la estabilidad de las distribuciones n variables respuesta Yi , i = 1, · · · , n. Como todas estas distribuciones están relacionadas entre sà por un único vector de parámetros, la estabilidad de las primeras depende de la estabilidad de este último. De este modo, es claro que tanto el monitoreo de modelos de regresión como el de perfiles comparten el mismo propósito. Es asà como las técnicas usadas para monitorear perfiles pueden también usarse par monitorear acertadamente los modelos de regresión para tiempos de vida. Se presentan algunas metodologÃas para monitorear modelos de regresión para tiempos de vida con respuesta Weibull, dependiendo de cómo están conformadas los conjuntos de datos disponibles. El monitoreo del vector de parámetros de modelos de regresión Weibull permite hacer conclusiones acerca del valor medio de la variable respuesta. Se mostrará además que se puede encarar el monitoreo de modelos de regresión para tiempos de vida mediante el rediseño de las metodologÃas de control que comúnmente se usan para monitorear variables de calidad continuas o para monitorear perfiles. Cuando la respuesta no es censurada, se encontr´o que es posible adaptar las cartas de control convencionales para observaciones individuales de la caracterÃstica de calidad, al monitoreo del parámtero de forma de un modelo de regresión Weibull. Es posible también adaptar las metodologÃas de control usadas en el monitoreo de perfiles para monitorear todo el vector de parámetros que caracterizan los modelos de regresión Weibull. En ambos casos, el diseño de las cartas se basa en la normalidad asintótica del estimador máximo verosÃmil del vector de parámetros. Por consiguiente, se hace necesario implementar correcciones existentes a las estadÃsticas de monitoreo para que las cartas de control trabajen aceptablemente aún cuando no se disponga de conjuntos de datos lo suficientemente grandes. Cuando un mecanismo de censura a derecha de tipo I opera sobre los tiempos de vida, se puede realizar el monitoreo con la ayuda de cartas de control unilaterales de sumas acumuladas basadas en la estadÃstica de razón de verosimilitudes. Estos esquemas se pueden utilizar para monitorear uno o varios parámetros que conforman el vector de parámetros y prácticamente no tienen restricciones respecto a la cantidad de observaciones necesarias para realizar el monitoreo. Los estudios de simulación sugieren que estos esquemas son más efectivos que los métodos multivariados de promedios móviles ponderados exponencialmente cuando se desea detectar el deterioro de los procesos de calidad.Doctorad
Monitoring regression models for lifetimes
Abstract. Monitoring regression models for lifetimes The current study addresses the monitoring of regression models with response variable having a distribution for lifetimes. Certain aspects of this research have relevant importance. First of all, in most of the existing literature, monitoring regression models is treated as a special case of profile monitoring. However, especially in some industrial and healthcare applications, regression models can adequately represent process quality but cannot always be qualified as profiles. This is the case of regression models for lifetimes. The fact is that lifetimes can be measured just once at most in the same experimental unit. Consequently, the nature of responses while monitoring regression models is not multivariate necessarily. However, the main goal of monitoring regression models for lifetimes aims to check the stability of the distributions of n response variables Yi , i = 1, · · · , n. As all these distributions are linked by the same parameter vector, the stability of the formers depends on the one of the latter. Thus, it is clear that profile monitoring and regression monitoring share the same purpose. Techniques from profile monitoring can be used for successfully monitoring regression models for lifetimes as well. Some methodologies for monitoring Weibull regression models for lifetimes with common shape parameter and in phase II processes will be addressed depending on the composition of available regression data structures. The monitoring of the parameter vector characterizing the Weibull regression model allows us to make conclusions about the mean value of the response variable. It will be shown that the monitoring of regression models for lifetimes can be carried out by redesigning existing methods from monitoring continuous quality variables and profile monitoring. In the presence of uncensored lifetimes, it was found out that it is possible to adapt conventional control charts for single observations to the monitoring of the common shape parameter. It is also possible to adapt control techniques and methodologies from profile monitoring to the case of monitoring the entire parameter vector characterizing the basic model. In both cases, chart designing depends on the asymptotic normality of the maximum likelihood estimator of the parameter vector. Thus, it is necessary to implement some existing corrections to the monitoring statistics so that existing control charts work acceptably well when non-large enough data sets are available. When a type I right-censored mechanism is operating on lifetimes, the monitoring can be carried out with the help of one-sided likelihood ratio based cumulative sum control charts. Theese procedures can be used for monitoring one or more of the parameters in the parameter vector and has practically no restrictions respect to the dataset dimension needed for monitoring. Conducted simulations suggest that this chart is more effective than the multivariate exponentially weighted moving average method when detecting the deterioration of the process is wanted.Monitoreo de modelos de regresión para tiempos de vida El presente estudio se aborda el monitoreo de modelos de regresión para tiempos de vida. Ciertos aspectos de este trabajo son de crucial importancia. Como primera medida, en gran parte de la literatura especializada, el monitoreo de modelos de regresión se trata como un caso particular del monitoreo de perfiles. Sin embargo, existen muchas aplicaciones, especialmente en ingenierÃa y en cuidados en salud, en las cuales los modelos de regresión pueden caracterizar adecuadamente la calidad de los procesos pero no siempre pueden considerarse como perfiles. Es el caso de los modelos de regresión para tiempos de vida. El hecho es que, en general, un tiempo de vida puede medirse a lo sumo una vez en la misma unidad experimental. Consecuentemente, la naturaleza de las respuestas en el monitoreo de modelos de regresión no necesariamente es multivariada. Sin embargo, el objetivo principal del montireo de modelos regresión apunta a verificar la estabilidad de las distribuciones n variables respuesta Yi , i = 1, · · · , n. Como todas estas distribuciones están relacionadas entre sà por un único vector de parámetros, la estabilidad de las primeras depende de la estabilidad de este último. De este modo, es claro que tanto el monitoreo de modelos de regresión como el de perfiles comparten el mismo propósito. Es asà como las técnicas usadas para monitorear perfiles pueden también usarse par monitorear acertadamente los modelos de regresión para tiempos de vida. Se presentan algunas metodologÃas para monitorear modelos de regresión para tiempos de vida con respuesta Weibull, dependiendo de cómo están conformadas los conjuntos de datos disponibles. El monitoreo del vector de parámetros de modelos de regresión Weibull permite hacer conclusiones acerca del valor medio de la variable respuesta. Se mostrará además que se puede encarar el monitoreo de modelos de regresión para tiempos de vida mediante el rediseño de las metodologÃas de control que comúnmente se usan para monitorear variables de calidad continuas o para monitorear perfiles. Cuando la respuesta no es censurada, se encontr´o que es posible adaptar las cartas de control convencionales para observaciones individuales de la caracterÃstica de calidad, al monitoreo del parámtero de forma de un modelo de regresión Weibull. Es posible también adaptar las metodologÃas de control usadas en el monitoreo de perfiles para monitorear todo el vector de parámetros que caracterizan los modelos de regresión Weibull. En ambos casos, el diseño de las cartas se basa en la normalidad asintótica del estimador máximo verosÃmil del vector de parámetros. Por consiguiente, se hace necesario implementar correcciones existentes a las estadÃsticas de monitoreo para que las cartas de control trabajen aceptablemente aún cuando no se disponga de conjuntos de datos lo suficientemente grandes. Cuando un mecanismo de censura a derecha de tipo I opera sobre los tiempos de vida, se puede realizar el monitoreo con la ayuda de cartas de control unilaterales de sumas acumuladas basadas en la estadÃstica de razón de verosimilitudes. Estos esquemas se pueden utilizar para monitorear uno o varios parámetros que conforman el vector de parámetros y prácticamente no tienen restricciones respecto a la cantidad de observaciones necesarias para realizar el monitoreo. Los estudios de simulación sugieren que estos esquemas son más efectivos que los métodos multivariados de promedios móviles ponderados exponencialmente cuando se desea detectar el deterioro de los procesos de calidad.Doctorad
ISBIS 2016: Meeting on Statistics in Business and Industry
This Book includes the abstracts of the talks presented at the 2016 International Symposium on Business and Industrial Statistics, held at Barcelona, June 8-10, 2016, hosted at the Universitat Politècnica de Catalunya - Barcelona TECH, by the Department of Statistics and Operations Research. The location of the meeting was at ETSEIB Building (Escola Tecnica Superior d'Enginyeria Industrial) at Avda Diagonal 647.
The meeting organizers celebrated the continued success of ISBIS and ENBIS society, and the meeting draw together the international community of statisticians, both academics and industry professionals, who share the goal of making statistics the foundation for decision making in business and related applications. The Scientific Program Committee was constituted by:
David Banks, Duke University
AmÃlcar Oliveira, DCeT - Universidade Aberta and CEAUL
Teresa A. Oliveira, DCeT - Universidade Aberta and CEAUL
Nalini Ravishankar, University of Connecticut
Xavier Tort Martorell, Universitat Politécnica de Catalunya, Barcelona TECH
Martina Vandebroek, KU Leuven
Vincenzo Esposito Vinzi, ESSEC Business Schoo
Relative Survival Methods – Theory, Applications and Extensions to Monitoring
In cancer research, one is often interested in the part of the hazard which corresponds to the disease. If the cause of death is unknown as in cancer registry data, the standard methods in survival analysis do not distinguish between the mortality due to disease and other causes. This issue becomes the main motivation for the development of relative survival methods. First, the main concepts in relative survival are presented. Both non-parametric estimators and models of the excess hazard are studied and discussed. Simulation studies show that even if the Pohar-Perme method is an unbiased estimator of the so-called net survival, the traditional Ederer 2 estimator might still be preferable in certain situations due to its lower variance. When informative censoring is present, the degree of bias looks to be the same on average for both estimators.
When it comes to modelling of the excess hazard, we cover two different types of models. The first group corresponds to parametric models where the baseline excess hazard is a piecewise constant function. For real-life data, this is usually not the case and a more flexible and semi-parametric model based on the EM-algorithm is therefore considered. By simulation, the piecewise constant models still perform decent if the gradient of the baseline excess hazard is not large and there are enough data such that a finer splitting of the follow-up interval can be used in the estimation procedure.
In some situations, one might also want to monitor the excess hazard over time in order to detect a change. An approach based on methods from relative survival and statistical process control is proposed for this intention. Different simulation setups are used in order to illustrate the purpose of the method. Finally, most of the methods presented are applied to colon and rectum cancer data from the Norwegian Cancer Registry. Interesting results are obtained from the analysis. For instance, the effect of tumour location seems to vary between age groups. Similar arguments are observed related to cancer stage as well. The CUSUM charts show a clear improvement in the excess hazard over time, which agree with the results from non-parametric methods when stratified by diagnosis year period
Modelo de apoio à decisão para a manutenção condicionada de equipamentos produtivos
Doctoral Thesis for PhD degree in Industrial and Systems EngineeringIntroduction: This thesis describes a methodology to combine Bayesian control chart
and CBM (Condition-Based Maintenance) for developing a new integrated model. In
maintenance management, it is a challenging task for decision-maker to conduct an
appropriate and accurate decision. Proper and well-performed CBM models are
beneficial for maintenance decision making. The integration of Bayesian control chart
and CBM is considered as an intelligent model and a suitable strategy for forecasting
items failures as well as allow providing an effectiveness maintenance cost. CBM
models provides lower inventory costs for spare parts, reduces unplanned outage, and
minimize the risk of catastrophic failure, avoiding high penalties associated with losses
of production or delays, increasing availability. However, CBM models need new
aspects and the integration of new type of information in maintenance modeling that can
improve the results. Objective: The thesis aims to develop a new methodology based on
Bayesian control chart for predicting failures of item incorporating simultaneously two
types of data: key quality control measurement and equipment condition parameters. In
other words, the project research questions are directed to give the lower maintenance
costs for real process control. Method: The mathematical approach carried out in this
study for developing an optimal Condition Based Maintenance policy included the
Weibull analysis for verifying the Markov property, Delay time concept used for
deterioration modeling and PSO and Monte Carlo simulation. These models are used for
finding the upper control limit and the interval monitoring that minimizes the
(maintenance) cost function. Result: The main contribution of this thesis is that the
proposed model performs better than previous models in which the hypothesis of using
simultaneously data about condition equipment parameters and quality control
measurements improve the effectiveness of integrated model Bayesian control chart for
Condition Based Maintenance.Introdução: Esta tese descreve uma metodologia para combinar Bayesian control chart
e CBM (Condition- Based Maintenance) para desenvolver um novo modelo integrado.
Na gestão da manutenção, é importante que o decisor possa tomar decisões apropriadas
e corretas. Modelos CBM bem concebidos serão muito benéficos nas tomadas de
decisão sobre manutenção. A integração dos gráficos de controlo Bayesian e CBM é
considerada um modelo inteligente e uma estratégica adequada para prever as falhas de
componentes bem como produzir um controlo de custos de manutenção. Os modelos
CBM conseguem definir custos de inventário mais baixos para as partes de substituição,
reduzem interrupções não planeadas e minimizam o risco de falhas catastróficas,
evitando elevadas penalizações associadas a perdas de produção ou atrasos, aumentando
a disponibilidade. Contudo, os modelos CBM precisam de alterações e a integração de
novos tipos de informação na modelação de manutenção que permitam melhorar os
resultados.Objetivos: Esta tese pretende desenvolver uma nova metodologia baseada
Bayesian control chart para prever as falhas de partes, incorporando dois tipos de
dados: medições-chave de controlo de qualidade e parâmetros de condição do
equipamento. Por outras palavras, as questões de investigação são direcionadas para
diminuir custos de manutenção no processo de controlo.Métodos: Os modelos
matemáticos implementados neste estudo para desenvolver uma polÃtica ótima de CBM
incluÃram a análise de Weibull para verificação da propriedade de Markov, conceito de
atraso de tempo para a modelação da deterioração, PSO e simulação de Monte Carlo.
Estes modelos são usados para encontrar o limite superior de controlo e o intervalo de
monotorização para minimizar a função de custos de manutenção.Resultados: A
principal contribuição desta tese é que o modelo proposto melhora os resultados dos
modelos anteriores, baseando-se na hipótese de que, usando simultaneamente dados dos
parâmetros dos equipamentos e medições de controlo de qualidade. Assim obtém-se
uma melhoria a eficácia do modelo integrado de Bayesian control chart para a
manutenção condicionada
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