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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.
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.
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