In teaching an elementary course in stochastic processes it was noticed that many seemingly deep results in point processes are readily accessible by the device of representing them in terms of random gap lengths between points. The possibility of representing point processes in terms of sequences of random variables rather than probability measures makes them mathemati cally simpler than general stochastic processes. Point processes can be studied using only the tools of elementary probability, that is the joint distributions of finitely many random variables. Given the wide applicability of point process models and the difficulty of access by the measure-theoretic route, it was determined that the simpler representation is of sufficient expository im portance to deserve emphasis. The present book is the result: it is specialized and short and therefore is called a monograph. In its development the material has been taught to several classes with pleasing results. Students have apparently understood theorems which by other methods appear difficult and deep. A few of the results, particularly on reliability, safety assessment and clustering, are original applied research. An alternative title for this monograph might be 'Point processes: What they are and what they are good for.

This handbook studies the combination of various methods of designing for reliability, availability, maintainability and safety, as well as the latest techniques in probability and possibility modeling, mathematical algorithmic modeling, evolutionary algorithmic modeling, symbolic logic modeling, artificial intelligence modeling and object-oriented computer modeling.

Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with recent theoretical findings of the authors. It also presents numerous examples that illustrate how general results and approaches are applied to stochastic description of repairable systems and systems operating in a random environment modelled by shock processes. The real life objects are operating in a changing, random environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The Poisson (homogeneous and nonhomogeneous) process, the renewal process and their generalizations are considered as models for external shocks affecting an operating system. At the same time these processes model the consecutive failure/repair times of repairable engineering systems. Perfect, minimal and intermediate (imperfect) repairs are discussed in this respect. Covering material previously available only in the journal literature, Point Processes for Reliability Analysis provides a survey of recent developments in this area which will be invaluable to researchers and advanced students in reliability engineering and applied mathematics.

This graduate-level textbook provides a straight-forward and mathematically rigorous introduction to the standard theory of point processes. The author's aim is to present an account which concentrates on the essentials and which places an emphasis on conveying an intuitive understanding of the subject. As a result, it provides a clear presentation of how statistical ideas can be viewed from this perspective and particular topics covered include the theory of extreme values and sampling from finite populations. Prerequisites are that the reader has a basic grounding in the mathematical theory of probability and statistics, but otherwise the book is self-contained. It arises from courses given by the author over a number of years and includes numerous exercises ranging from simple computations to more challenging explorations of ideas from the text.

Within the last fifty years the performance requirements for technical objects and systems were supplemented with: customer expectations (quality), abilities to prevent the loss of the object properties in operation time (reliability and maintainability), protection against the effects of undesirable events (safety and security) and the ability to

Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.

An effective reliability programme is an essential component of every product's design, testing and efficient production. From the failure analysis of a microelectronic device to software fault tolerance and from the accelerated life testing of mechanical components to hardware verification, a common underlying philosophy of reliability applies. Defining both fundamental and applied work across the entire systems reliability arena, this state-of-the-art reference presents methodologies for quality, maintainability and dependability. Featuring: Contributions from 60 leading reliability experts in academia and industry giving comprehensive and authoritative coverage. A distinguished international Editorial Board ensuring clarity and precision throughout. Extensive references to the theoretical foundations, recent research and future directions described in each chapter. Comprehensive subject index providing maximum utility to the reader. Applications and examples across all branches of engineering including IT, power, automotive and aerospace sectors. The handbook's cross-disciplinary scope will ensure that it serves as an indispensable tool for researchers in industrial, electrical, electronics, computer, civil, mechanical and systems engineering. It will also aid professional engineers to find creative reliability solutions and management to evaluate systems reliability and to improve processes. For student research projects it will be the ideal starting point whether addressing basic questions in communications and electronics or learning advanced applications in micro-electro-mechanical systems (MEMS), manufacturing and high-assurance engineering systems.

This book provides the latest research advances in the field of system reliability assurance and engineering. It contains reference material for applications of reliability in system engineering, offering a theoretical sound background with adequate numerical illustrations. Included are concepts pertaining to reliability analysis, assurance techniques and methodologies, tools, and practical applications of system reliability modeling and allocation. The collection discusses various soft computing techniques like artificial intelligence and particle swarm optimization approach for reliability assessment. Importance of differentiating between the optimal release time and testing stop time of the software has been explicitly discussed and presented in the book. Features: Creates understanding of the costs associated with complex systems Covers reliability measurement of engineering systems Incorporates an efficient effort-based expenditure policy incorporating cost and reliability criteria Provides information for optimal testing stop and release time of software system Presents software performance and security layout Addresses reliability prediction and its maintenance through advanced analytics techniques Overall, System Reliability Management: Solutions and Techniques is a collaborative and interdisciplinary approach for better communication of problems and solutions to increase the performance of the system for better utilization and resource management.

This volume consists of twenty-four papers selected by the editors from the sixty-one papers presented at the 1st International Conference on Mathemati cal Methods in Reliability held at the Politehnica University of Bucharest from 16 to 19 September 1997. The papers have been divided into three sections: statistical methods, probabilistic methods, and special techniques and appli cations. Of course, as with any classification, some papers could be as well assigned to other sections. Problems in reliability are encountered in items in everyday usage. Relia bility is an important feature of household appliances, cars, telephones, power supplies, and so on, whether viewed from the vantage of the producer or the consumer. Important decisions are based on the reliability of the product. Obtaining systems that perform adequately for a specified period of time in a given environment is an important goal for both government and industry. Hence study and use of reliability theory, which can be applied in the research, development, and production phases of a system to enable the user to evaluate and improve performance, is a worthwhile venture. If reliability theory is to be useful, it must be quantitative in nature, because reliability must be demonstra ble. Subsequently probability and statistics, among others, play an important part in its development.

Handbook for the computation and empirical estimation of reliability. Introduces an incomparable volume of easily applicable, cutting-edge results originated by prominent Russian reliability specialists. Completely covers probabilistic reliability, statistical reliability and optimization with simple, step-by-step, numerical examples. Offers a broad range of applications in engineering, operations research, cost analysis and project management. Explores reliability software extensively. Includes appendices with summary reviews of mathematical and statistical fundamentals.