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.

Safety and Reliability Modeling and Its Applications combines work by leading researchers in engineering, statistics and mathematics who provide innovative methods and solutions for this fast-moving field. Safety and reliability analysis is one of the most multidimensional topics in engineering today. Its rapid development has created many opportunities and challenges for both industrialists and academics, while also completely changing the global design and systems engineering environment. As more modeling tasks can now be undertaken within a computer environment using simulation and virtual reality technologies, this book helps readers understand the number and variety of research studies focusing on this important topic. The book addresses these important recent developments, presenting new theoretical issues that were not previously presented in the literature, along with solutions to important practical problems and case studies that illustrate how to apply the methodology. Uses case studies from industry practice to explain innovative solutions to real world safety and reliability problems Addresses the full interdisciplinary range of topics that influence this complex field Provides brief introductions to important concepts, including stochastic reliability and Bayesian methods

Promotes better ways to diagnose, maintain, and improve existing systems. Existing reliability evaluation models are examined with respect to today's complicated engineering systems that have hundreds of thousands of integrated component designs.

Software reliability is one of the most important characteristics of software product quality. Its measurement and management technologies during the software product life cycle are essential to produce and maintain quality/reliable software systems. Part 1 of this book introduces several aspects of software reliability modeling and its applications. Hazard rate and nonhomogeneous Poisson process (NHPP) models are investigated particularly for quantitative software reliability assessment. Further, imperfect debugging and software availability models are discussed with reference to incorporating practical factors of dynamic software behavior. Three software management problems are presented as application technologies of software reliability models: the optimal software release problem, the statistical testing-progress control, and the optimal testing-effort allocation problem. Part 2 of the book describes several recent developments in software reliability modeling and their applications as quantitative techniques for software quality/reliability measurement and assessment. The discussion includes a quality engineering analysis of human factors affecting software reliability during the design review phase, which is the upper stream of software development, as well as software reliability growth models based on stochastic differential equations and discrete calculus during the testing phase, which is the lower stream. The final part of the book provides an illustration of quality-oriented software management analysis by applying the multivariate analysis method and the existing software reliability growth models to actual process monitoring data.

This book summarizes the recent advances in software reliability modelling. Almost all the existing models are classified and the most interesting models are described in detail.Because of the application of software in many industrial, military and commercial systems, software reliability has become an important research area. Although there are many models and results appeared in different journals and conference proceedings, there is a lack of systematic publications on this subject. The aim of this book is to provide an overview of this area and provide software reliability researchers and analysts with a systematic study of the existing results. This book can also be used as a reference book for other software engineers and reliability theoreticians interested in this area.

This book summarizes the recent advances in software reliability modelling. Almost all the existing models are classified and the most interesting models are described in detail. Because of the application of software in many industrial, military and commercial systems, software reliability has become an important research area. Although there are many models and results appeared in different journals and conference proceedings, there is a lack of systematic publications on this subject. The aim of this book is to provide an overview of this area and provide software reliability researchers and analysts with a systematic study of the existing results. This book can also be used as a reference book for other software engineers and reliability theoreticians interested in this area. Contents: Introduction to Software ReliabilityElements of Software Reliability ModellingMarkov ModelsNonhomogeneous Poisson Process (NHPP) ModelsSome Static ModelsBayesian Analysis and ModellingSome Statistical Data Analysis TechniquesDetermination of Optimum Release TimeRecent Advances in Software Reliability Readership: Software engineers and reliability analysts. keywords:

Proceedings of the ISPRA Course Held November 25-29, 1985, Organized in Collaboration with the European Safety and Reliability Association-ESRA

The development of Reliability and Maintenance theory and applications has become major concerns of engineers and managers engaged in order to design and product systems that are highly reliable. This book aims to cover the ongoing research topics in computer system, reliability analysis, reliability applications and maintenance policies, so as to provide awareness for those who engage systems design, being students, technicians, or research engineers, as a reference guidebook.

This book presents the state-of-the-art methodology and detailed analytical models and methods used to assess the reliability of complex systems and related applications in statistical reliability engineering. It is a textbook based mainly on the author’s recent research and publications as well as experience of over 30 years in this field. The book covers a wide range of methods and models in reliability, and their applications, including: statistical methods and model selection for machine learning; models for maintenance and software reliability; statistical reliability estimation of complex systems; and statistical reliability analysis of k out of n systems, standby systems and repairable systems. Offering numerous examples and solved problems within each chapter, this comprehensive text provides an introduction to reliability engineering graduate students, a reference for data scientists and reliability engineers, and a thorough guide for researchers and instructors in the field.

The book deals with the application of various measures of information like the entropy, divergence, inaccuracy, etc. in modelling lifetimes of devices or equipment in reliability analysis. This is an emerging area of study and research during the last two decades and is of potential interest in many fields. In this work the classical measures of uncertainty are sufficiently modified to meet the needs of lifetime data analysis. The book provides an exhaustive collection of materials in a single volume to make it a comprehensive source of reference. The first treatise on the subject. It brings together the work that have appeared in journals on different disciplines. It will serve as a text for graduate students and practioners of special studies in information theory, as well as statistics and as a reference book for researchers. The book contains illustrative examples, tables and figures for clarifying the concepts and methodologies, the book is self-contained. It helps students to access information relevant to careers in industry, engineering, applied statistics, etc.