Optimal design and use of retry in fault tolerant real-time computer systems

A new method to determin an optimal retry policy and for use in retry of fault characterization is presented. An optimal retry policy for a given fault characteristic, which determines the maximum allowable retry durations to minimize the total task completion time was derived. The combined fault characterization and retry decision, in which the characteristics of fault are estimated simultaneously with the determination of the optimal retry policy were carried out. Two solution approaches were developed, one based on the point estimation and the other on the Bayes sequential decision. The maximum likelihood estimators are used for the first approach, and the backward induction for testing hypotheses in the second approach. Numerical examples in which all the durations associated with faults have monotone hazard functions, e.g., exponential, Weibull and gamma distributions are presented. These are standard distributions commonly used for modeling analysis and faults

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 ingeniería 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 sí 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 así como las técnicas usadas para monitorear perfiles pueden también usarse par monitorear acertadamente los modelos de regresión para tiempos de vida. Se presentan algunas metodologías 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 metodologías 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 característica de calidad, al monitoreo del parámtero de forma de un modelo de regresión Weibull. Es posible también adaptar las metodologías 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 verosímil del vector de parámetros. Por consiguiente, se hace necesario implementar correcciones existentes a las estadísticas 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 estadística 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

Attitudes towards old age and age of retirement across the world: findings from the future of retirement survey

The 21st century has been described as the first era in human history when the world will no longer be young and there will be drastic changes in many aspects of our lives including socio-demographics, financial and attitudes towards the old age and retirement. This talk will introduce briefly about the Global Ageing Survey (GLAS) 2004 and 2005 which is also popularly known as “The Future of Retirement”. These surveys provide us a unique data source collected in 21 countries and territories that allow researchers for better understanding the individual as well as societal changes as we age with regard to savings, retirement and healthcare. In 2004, approximately 10,000 people aged 18+ were surveyed in nine counties and one territory (Brazil, Canada, China, France, Hong Kong, India, Japan, Mexico, UK and USA). In 2005, the number was increased to twenty-one by adding Egypt, Germany, Indonesia, Malaysia, Poland, Russia, Saudi Arabia, Singapore, Sweden, Turkey and South Korea). Moreover, an additional 6320 private sector employers was surveyed in 2005, some 300 in each country with a view to elucidating the attitudes of employers to issues relating to older workers. The paper aims to examine the attitudes towards the old age and retirement across the world and will indicate some policy implications