"Failure Rate Modeling for Reliability and Risk" focuses on reliability theory, and to the failure rate (hazard rate, force of mortality) modeling and its generalizations to systems operating in a random environment and to repairable systems. The failure rate is one of the crucial probabilistic characteristics for a number of disciplines; including reliability, survival analysis, risk analysis and demography. The book presents a systematic study of the failure rate and related indices, and covers a number of important applications where the failure rate plays the major role. Applications in engineering systems are studied, together with some actuarial, biological and demographic examples. The book provides a survey of this broad and interdisciplinary subject which will be invaluable to researchers and advanced students in reliability engineering and applied statistics, as well as to demographers, econometricians, actuaries and many other mathematically oriented researchers.

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.

Focusing on shocks modeling, burn-in and heterogeneous populations, Stochastic Modeling for Reliability naturally combines these three topics in the unified stochastic framework and presents numerous practical examples that illustrate recent theoretical findings of the authors. The populations of manufactured items in industry are usually heterogeneous. However, the conventional reliability analysis is performed under the implicit assumption of homogeneity, which can result in distortion of the corresponding reliability indices and various misconceptions. Stochastic Modeling for Reliability fills this gap and presents the basics and further developments of reliability theory for heterogeneous populations. Specifically, the authors consider burn-in as a method of elimination of 'weak' items from heterogeneous populations. The real life objects are operating in a changing 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 basic theory for Poisson shock processes is developed and also shocks as a method of burn-in and of the environmental stress screening for manufactured items are considered. Stochastic Modeling for Reliability introduces and explores the concept of burn-in in heterogeneous populations and its recent development, providing a sound reference for reliability engineers, applied mathematicians, product managers and manufacturers alike.

Focusing on shocks modeling, burn-in and heterogeneous populations, Stochastic Modeling for Reliability naturally combines these three topics in the unified stochastic framework and presents numerous practical examples that illustrate recent theoretical findings of the authors. The populations of manufactured items in industry are usually heterogeneous. However, the conventional reliability analysis is performed under the implicit assumption of homogeneity, which can result in distortion of the corresponding reliability indices and various misconceptions. Stochastic Modeling for Reliability fills this gap and presents the basics and further developments of reliability theory for heterogeneous populations. Specifically, the authors consider burn-in as a method of elimination of 'weak' items from heterogeneous populations. The real life objects are operating in a changing 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 basic theory for Poisson shock processes is developed and also shocks as a method of burn-in and of the environmental stress screening for manufactured items are considered. Stochastic Modeling for Reliability introduces and explores the concept of burn-in in heterogeneous populations and its recent development, providing a sound reference for reliability engineers, applied mathematicians, product managers and manufacturers alike.

Failure Rate Modeling for Reliability and Risk focuses on reliability theory, and to the failure rate (hazard rate, force of mortality) modeling and its generalizations to systems operating in a random environment and to repairable systems. The failure rate is one of the crucial probabilistic characteristics for a number of disciplines; including reliability, survival analysis, risk analysis and demography. The book presents a systematic study of the failure rate and related indices, and covers a number of important applications where the failure rate plays the major role. Applications in engineering systems are studied, together with some actuarial, biological and demographic examples. The book provides a survey of this broad and interdisciplinary subject which will be invaluable to researchers and advanced students in reliability engineering and applied statistics, as well as to demographers, econometricians, actuaries and many other mathematically oriented researchers.

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.