An optimization of on-line monitoring of simple linear and polynomial quality functions

This research aims to introduce a number of contributions for enhancing the statistical performance of some of Phase II linear and polynomial profile monitoring techniques. For linear profiles the idea of variable sampling size (VSS) and variable sampling interval (VSI) have been extended from multivariate control charts to the profile monitoring framework to enhance the power of the traditional T^2 chart in detecting shifts in linear quality models. Finding the optimal settings of the proposed schemes has been formulated as an optimization problem solved by using a Genetic Approach (GA). Here the average time to signal (ATS) and the average run length (ARL) are regarded as the objective functions, and ATS and ARL approximations, based on Markov Chain Principals, are extended and modified to capture the special structure of the profile monitoring. Furthermore,the performances of the proposed control schemes are compared with their fixed sampling counterparts for different shift levels in the parameters. The extensive comparison studies reveal the potentials of the proposed schemes in enhancing the performance of T^2 control chart when a process yields a simple linear profile. For polynomial profiles, where the linear regression model is not sufficient, the relationship between the parameters of the original and orthogonal polynomial quality profiles is considered and utilized to enhance the power of the orthogonal polynomial method (EWMA4). The problem of finding the optimal set of explanatory variable minimizing the average run length is described by a mathematical model and solved using the Genetic Approach. In the case that the shift in the second or the third parameter is the only shift of interest, the simulation results show a significant reduction in the mean of the run length distribution of the EWMA4 technique

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 Amílcar 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

Run Rules-Based EWMA Charts for Efficient Monitoring of Profile Parameters

In usual quality control methods, the quality of a process or product is evaluated by monitoring one or more quality characteristics using their corresponding distributions. However, when the quality characteristic is defined through the relationship between one or more response and independent variables, the regime is referred to as profiles monitoring. In this article, we improve the performance of the Exponentially Weighted Moving Average Range (EWMAR) control charts, which are implemented for monitoring linear profiles (i.e., intercept, slope and average residual between sample and reference lines) by integrating them with run rules in order to quickly detect various magnitudes of shifts in profile parameters. The validation of the proposed control chart is accomplished by examining its performance using the average run length (ARL) criteria. The proposed EWMAR chart with run rules exhibits a much better performance in detecting small and decreasing shifts than the other competing charts. Finally, an example from multivariate manufacturing industry is employed to illustrate the superiority of the EWMAR chart with run rules. 2013 IEEE.Scopu

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

Exact asymptotic distribution of change-point mle for change in the mean of Gaussian sequences

We derive exact computable expressions for the asymptotic distribution of the change-point mle when a change in the mean occurred at an unknown point of a sequence of time-ordered independent Gaussian random variables. The derivation, which assumes that nuisance parameters such as the amount of change and variance are known, is based on ladder heights of Gaussian random walks hitting the half-line. We then show that the exact distribution easily extends to the distribution of the change-point mle when a change occurs in the mean vector of a multivariate Gaussian process. We perform simulations to examine the accuracy of the derived distribution when nuisance parameters have to be estimated as well as robustness of the derived distribution to deviations from Gaussianity. Through simulations, we also compare it with the well-known conditional distribution of the mle, which may be interpreted as a Bayesian solution to the change-point problem. Finally, we apply the derived methodology to monthly averages of water discharges of the Nacetinsky creek, Germany.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS294 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Contributions to statistical methods of process monitoring and adjustment

Ph.DDOCTOR OF PHILOSOPH