Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Reliability modelling and verification of manufacturing processes based on process knowledge management

Reliability modelling and verification is indispensable in modern manufacturing, especially for product development risk reduction. Based on the discussion of the deficiencies of traditional reliability modelling methods for process reliability, a novel modelling method is presented herein that draws upon a knowledge network of process scenarios based on the analytic network process (ANP). An integration framework of manufacturing process reliability and product quality is presented together with a product development and reliability verification process. According to the roles of key characteristics (KCs) in manufacturing processes, KCs are organised into four clusters, that is, product KCs, material KCs, operation KCs and equipment KCs, which represent the process knowledge network of manufacturing processes. A mathematical model and algorithm is developed for calculating the reliability requirements of KCs with respect to different manufacturing process scenarios. A case study on valve-sleeve component manufacturing is provided as an application example of the new reliability modelling and verification procedure. This methodology is applied in the valve-sleeve component manufacturing processes to manage and deploy production resources.

Characterization of Probability Distributions by Variance Bounds and its Applications

Department of Statistics, Cochin University of Science and Technology

Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

A novel repair model for imperfect maintenance

Commonly used repair rate models for repairable systems in the reliability literature are renewal processes, generalised renewal processes or non-homogeneous Poisson processes. In addition to these models, geometric processes (GP) are studied occasionally. The GP, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensities. This paper deals with the reliability modelling of failure processes for repairable systems where the failure intensity shows a bathtub-type non-monotonic behaviour. A new stochastic process, i.e. an extended Poisson process, is introduced in this paper. Reliability indices are presented, and the parameters of the new process are estimated. Experimental results on a data set demonstrate the validity of the new process.

A novel repair model for imperfect maintenance

The basic repair rate models for repairable systems may be homogeneous Poisson processes, renewal processes or nonhomogeneous Poisson processes. In addition to these models, geometric processes are studied occasionally. Geometric processes, however, can only model systems with monotonously changing (increasing, decreasing or constant) failure intensity. This paper deals with the reliability modelling of the failure process of repairable systems when the failure intensity shows a bathtub type non-monotonic behaviour. A new stochastic process, an extended Poisson process, is introduced. Reliability indices and parameter estimation are presented. A comparison of this model with other repair models based on a dataset is made.

Modelling the effects of row configuration on sorghum yield reliability in north-eastern Australia

In recent years, many sorghum producers in the more marginal (

Bridging the gap between different statistical approaches: An integrated framework for modelling

This paper proposes a template for modelling complex datasets that integrates traditional statistical modelling approaches with more recent advances in statistics and modelling through an exploratory framework. Our approach builds on the well-known and long standing traditional idea of 'good practice in statistics' by establishing a comprehensive framework for modelling that focuses on exploration, prediction, interpretation and reliability assessment, a relatively new idea that allows individual assessment of predictions. The integrated framework we present comprises two stages. The first involves the use of exploratory methods to help visually understand the data and identify a parsimonious set of explanatory variables. The second encompasses a two step modelling process, where the use of non-parametric methods such as decision trees and generalized additive models are promoted to identify important variables and their modelling relationship with the response before a final predictive model is considered. We focus on fitting the predictive model using parametric, non-parametric and Bayesian approaches. This paper is motivated by a medical problem where interest focuses on developing a risk stratification system for morbidity of 1,710 cardiac patients given a suite of demographic, clinical and preoperative variables. Although the methods we use are applied specifically to this case study, these methods can be applied across any field, irrespective of the type of response.

The tree cut and merge algorithm for estimation of network reliability

This article presents Monte Carlo techniques for estimating network reliability. For highly reliable networks, techniques based on graph evolution models provide very good performance. However, they are known to have significant simulation cost. An existing hybrid scheme (based on partitioning the time space) is available to speed up the simulations; however, there are difficulties with optimizing the important parameter associated with this scheme. To overcome these difficulties, a new hybrid scheme (based on partitioning the edge set) is proposed in this article. The proposed scheme shows orders of magnitude improvement of performance over the existing techniques in certain classes of network. It also provides reliability bounds with little overhead.

New developments and applications in modelling occupational exposure to airborne contaminants

Résumé: L'évaluation de l'exposition aux nuisances professionnelles représente une étape importante dans l'analyse de poste de travail. Les mesures directes sont rarement utilisées sur les lieux même du travail et l'exposition est souvent estimée sur base de jugements d'experts. Il y a donc un besoin important de développer des outils simples et transparents, qui puissent aider les spécialistes en hygiène industrielle dans leur prise de décision quant aux niveaux d'exposition. L'objectif de cette recherche est de développer et d'améliorer les outils de modélisation destinés à prévoir l'exposition. Dans un premier temps, une enquête a été entreprise en Suisse parmi les hygiénistes du travail afin d'identifier les besoins (types des résultats, de modèles et de paramètres observables potentiels). Il a été constaté que les modèles d'exposition ne sont guère employés dans la pratique en Suisse, l'exposition étant principalement estimée sur la base de l'expérience de l'expert. De plus, l'émissions de polluants ainsi que leur dispersion autour de la source ont été considérés comme des paramètres fondamentaux. Pour tester la flexibilité et la précision des modèles d'exposition classiques, des expériences de modélisations ont été effectuées dans des situations concrètes. En particulier, des modèles prédictifs ont été utilisés pour évaluer l'exposition professionnelle au monoxyde de carbone et la comparer aux niveaux d'exposition répertoriés dans la littérature pour des situations similaires. De même, l'exposition aux sprays imperméabilisants a été appréciée dans le contexte d'une étude épidémiologique sur une cohorte suisse. Dans ce cas, certains expériences ont été entreprises pour caractériser le taux de d'émission des sprays imperméabilisants. Ensuite un modèle classique à deux-zone a été employé pour évaluer la dispersion d'aérosol dans le champ proche et lointain pendant l'activité de sprayage. D'autres expériences ont également été effectuées pour acquérir une meilleure compréhension des processus d'émission et de dispersion d'un traceur, en se concentrant sur la caractérisation de l'exposition du champ proche. Un design expérimental a été développé pour effectuer des mesures simultanées dans plusieurs points d'une cabine d'exposition, par des instruments à lecture directe. Il a été constaté que d'un point de vue statistique, la théorie basée sur les compartiments est sensée, bien que l'attribution à un compartiment donné ne pourrait pas se faire sur la base des simples considérations géométriques. Dans une étape suivante, des données expérimentales ont été collectées sur la base des observations faites dans environ 100 lieux de travail différents: des informations sur les déterminants observés ont été associées aux mesures d'exposition des informations sur les déterminants observés ont été associé. Ces différentes données ont été employées pour améliorer le modèle d'exposition à deux zones. Un outil a donc été développé pour inclure des déterminants spécifiques dans le choix du compartiment, renforçant ainsi la fiabilité des prévisions. Toutes ces investigations ont servi à améliorer notre compréhension des outils des modélisations ainsi que leurs limitations. L'intégration de déterminants mieux adaptés aux besoins des experts devrait les inciter à employer cet outil dans leur pratique. D'ailleurs, en augmentant la qualité des outils des modélisations, cette recherche permettra non seulement d'encourager leur utilisation systématique, mais elle pourra également améliorer l'évaluation de l'exposition basée sur les jugements d'experts et, par conséquent, la protection de la santé des travailleurs. Abstract Occupational exposure assessment is an important stage in the management of chemical exposures. Few direct measurements are carried out in workplaces, and exposures are often estimated based on expert judgements. There is therefore a major requirement for simple transparent tools to help occupational health specialists to define exposure levels. The aim of the present research is to develop and improve modelling tools in order to predict exposure levels. In a first step a survey was made among professionals to define their expectations about modelling tools (what types of results, models and potential observable parameters). It was found that models are rarely used in Switzerland and that exposures are mainly estimated from past experiences of the expert. Moreover chemical emissions and their dispersion near the source have also been considered as key parameters. Experimental and modelling studies were also performed in some specific cases in order to test the flexibility and drawbacks of existing tools. In particular, models were applied to assess professional exposure to CO for different situations and compared with the exposure levels found in the literature for similar situations. Further, exposure to waterproofing sprays was studied as part of an epidemiological study on a Swiss cohort. In this case, some laboratory investigation have been undertaken to characterize the waterproofing overspray emission rate. A classical two-zone model was used to assess the aerosol dispersion in the near and far field during spraying. Experiments were also carried out to better understand the processes of emission and dispersion for tracer compounds, focusing on the characterization of near field exposure. An experimental set-up has been developed to perform simultaneous measurements through direct reading instruments in several points. It was mainly found that from a statistical point of view, the compartmental theory makes sense but the attribution to a given compartment could ñó~be done by simple geometric consideration. In a further step the experimental data were completed by observations made in about 100 different workplaces, including exposure measurements and observation of predefined determinants. The various data obtained have been used to improve an existing twocompartment exposure model. A tool was developed to include specific determinants in the choice of the compartment, thus largely improving the reliability of the predictions. All these investigations helped improving our understanding of modelling tools and identify their limitations. The integration of more accessible determinants, which are in accordance with experts needs, may indeed enhance model application for field practice. Moreover, while increasing the quality of modelling tool, this research will not only encourage their systematic use, but might also improve the conditions in which the expert judgments take place, and therefore the workers `health protection.

Modelling of weather radar echoes from anomalous propagation using a hybrid parabolic equation method and NWP model data

Contamination of weather radar echoes by anomalous propagation (anaprop) mechanisms remains a serious issue in quality control of radar precipitation estimates. Although significant progress has been made identifying clutter due to anaprop there is no unique method that solves the question of data reliability without removing genuine data. The work described here relates to the development of a software application that uses a numerical weather prediction (NWP) model to obtain the temperature, humidity and pressure fields to calculate the three dimensional structure of the atmospheric refractive index structure, from which a physically based prediction of the incidence of clutter can be made. This technique can be used in conjunction with existing methods for clutter removal by modifying parameters of detectors or filters according to the physical evidence for anomalous propagation conditions. The parabolic equation method (PEM) is a well established technique for solving the equations for beam propagation in a non-uniformly stratified atmosphere, but although intrinsically very efficient, is not sufficiently fast to be practicable for near real-time modelling of clutter over the entire area observed by a typical weather radar. We demonstrate a fast hybrid PEM technique that is capable of providing acceptable results in conjunction with a high-resolution terrain elevation model, using a standard desktop personal computer. We discuss the performance of the method and approaches for the improvement of the model profiles in the lowest levels of the troposphere.