Semi Markov Processes And Reliability

Author : N. Limnios,G. Oprisan
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 47,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461201618

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Semi-Markov Processes and Reliability by N. Limnios,G. Oprisan Pdf

At first there was the Markov property. The theory of stochastic processes, which can be considered as an exten sion of probability theory, allows the modeling of the evolution of systems through the time. It cannot be properly understood just as pure mathemat ics, separated from the body of experience and examples that have brought it to life. The theory of stochastic processes entered a period of intensive develop ment, which is not finished yet, when the idea of the Markov property was brought in. Not even a serious study of the renewal processes is possible without using the strong tool of Markov processes. The modern theory of Markov processes has its origins in the studies by A. A: Markov (1856-1922) of sequences of experiments "connected in a chain" and in the attempts to describe mathematically the physical phenomenon known as Brownian mo tion. Later, many generalizations (in fact all kinds of weakenings of the Markov property) of Markov type stochastic processes were proposed. Some of them have led to new classes of stochastic processes and useful applications. Let us mention some of them: systems with complete connections [90, 91, 45, 86]; K-dependent Markov processes [44]; semi-Markov processes, and so forth. The semi-Markov processes generalize the renewal processes as well as the Markov jump processes and have numerous applications, especially in relia bility.

Author : Nikolaos Limnios,Gheorghe Oprișan
Publisher : Unknown
Page : 222 pages
File Size : 51,9 Mb
Release : 2001
Category : Markov processes
ISBN : 3764341963

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Semi-Markov Processes and Reliability by Nikolaos Limnios,Gheorghe Oprișan Pdf

Author : Franciszek Grabski
Publisher : Elsevier
Page : 270 pages
File Size : 40,6 Mb
Release : 2014-09-25
Category : Technology & Engineering
ISBN : 9780128006597

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Semi-Markov Processes: Applications in System Reliability and Maintenance by Franciszek Grabski Pdf

Semi-Markov Processes: Applications in System Reliability and Maintenance is a modern view of discrete state space and continuous time semi-Markov processes and their applications in reliability and maintenance. The book explains how to construct semi-Markov models and discusses the different reliability parameters and characteristics that can be obtained from those models. The book is a useful resource for mathematicians, engineering practitioners, and PhD and MSc students who want to understand the basic concepts and results of semi-Markov process theory. Clearly defines the properties and theorems from discrete state Semi-Markov Process (SMP) theory. Describes the method behind constructing Semi-Markov (SM) models and SM decision models in the field of reliability and maintenance. Provides numerous individual versions of SM models, including the most recent and their impact on system reliability and maintenance.

Author : Jacques Janssen
Publisher : Springer Science & Business Media
Page : 572 pages
File Size : 53,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489905741

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Semi-Markov Models by Jacques Janssen Pdf

This book is the result of the International Symposium on Semi Markov Processes and their Applications held on June 4-7, 1984 at the Universite Libre de Bruxelles with the help of the FNRS (Fonds National de la Recherche Scientifique, Belgium), the Ministere de l'Education Nationale (Belgium) and the Bernoulli Society for Mathe matical Statistics and Probability. This international meeting was planned to make a state of the art for the area of semi-Markov theory and its applications, to bring together researchers in this field and to create a platform for open and thorough discussion. Main themes of the Symposium are the first ten sections of this book. The last section presented here gives an exhaustive biblio graphy on semi-Markov processes for the last ten years. Papers selected for this book are all invited papers and in addition some contributed papers retained after strong refereeing. Sections are I. Markov additive processes and regenerative systems II. Semi-Markov decision processes III. Algorithmic and computer-oriented approach IV. Semi-Markov models in economy and insurance V. Semi-Markov processes and reliability theory VI. Simulation and statistics for semi-Markov processes VII. Semi-Markov processes and queueing theory VIII. Branching IX. Applications in medicine X. Applications in other fields v PREFACE XI. A second bibliography on semi-Markov processes It is interesting to quote that sections IV to X represent a good sample of the main applications of semi-Markov processes i. e.

Author : Jacques Janssen,Raimondo Manca
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 41,7 Mb
Release : 2006-02-08
Category : Mathematics
ISBN : 9780387295480

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Applied Semi-Markov Processes by Jacques Janssen,Raimondo Manca Pdf

Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems. The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes. Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.

Author : Vlad Stefan Barbu,Nikolaos Limnios
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 44,7 Mb
Release : 2009-01-07
Category : Mathematics
ISBN : 9780387731735

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Semi-Markov Chains and Hidden Semi-Markov Models toward Applications by Vlad Stefan Barbu,Nikolaos Limnios Pdf

Here is a work that adds much to the sum of our knowledge in a key area of science today. It is concerned with the estimation of discrete-time semi-Markov and hidden semi-Markov processes. A unique feature of the book is the use of discrete time, especially useful in some specific applications where the time scale is intrinsically discrete. The models presented in the book are specifically adapted to reliability studies and DNA analysis. The book is mainly intended for applied probabilists and statisticians interested in semi-Markov chains theory, reliability and DNA analysis, and for theoretical oriented reliability and bioinformatics engineers.

Author : Jacques Janssen,Raimondo Manca
Publisher : Springer Science & Business Media
Page : 441 pages
File Size : 44,8 Mb
Release : 2007-05-15
Category : Mathematics
ISBN : 9780387707303

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Semi-Markov Risk Models for Finance, Insurance and Reliability by Jacques Janssen,Raimondo Manca Pdf

Everyone working in related fields from applied mathematicians to statisticians to actuaries and operations researchers will find this a brilliantly useful practical text. The book presents applications of semi-Markov processes in finance, insurance and reliability, using real-life problems as examples. After a presentation of the main probabilistic tools necessary for understanding of the book, the authors show how to apply semi-Markov processes in finance, starting from the axiomatic definition and continuing eventually to the most advanced financial tools.

Author : Jacques Janssen,Nikolaos Limnios
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 52,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332886

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Semi-Markov Models and Applications by Jacques Janssen,Nikolaos Limnios Pdf

This book presents a selection of papers presented to the Second Inter national Symposium on Semi-Markov Models: Theory and Applications held in Compiegne (France) in December 1998. This international meeting had the same aim as the first one held in Brussels in 1984 : to make, fourteen years later, the state of the art in the field of semi-Markov processes and their applications, bring together researchers in this field and also to stimulate fruitful discussions. The set of the subjects of the papers presented in Compiegne has a lot of similarities with the preceding Symposium; this shows that the main fields of semi-Markov processes are now well established particularly for basic applications in Reliability and Maintenance, Biomedicine, Queue ing, Control processes and production. A growing field is the one of insurance and finance but this is not really a surprising fact as the problem of pricing derivative products represents now a crucial problem in economics and finance. For example, stochastic models can be applied to financial and insur ance models as we have to evaluate the uncertainty of the future market behavior in order, firstly, to propose different measures for important risks such as the interest risk, the risk of default or the risk of catas trophe and secondly, to describe how to act in order to optimize the situation in time. Recently, the concept of VaR (Value at Risk) was "discovered" in portfolio theory enlarging so the fundamental model of Markowitz.

Author : Toshio Nakagawa
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 47,7 Mb
Release : 2011-05-27
Category : Technology & Engineering
ISBN : 9780857292742

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Stochastic Processes by Toshio Nakagawa Pdf

Reliability theory is of fundamental importance for engineers and managers involved in the manufacture of high-quality products and the design of reliable systems. In order to make sense of the theory, however, and to apply it to real systems, an understanding of the basic stochastic processes is indispensable. As well as providing readers with useful reliability studies and applications, Stochastic Processes also gives a basic treatment of such stochastic processes as: the Poisson process, the renewal process, the Markov chain, the Markov process, and the Markov renewal process. Many examples are cited from reliability models to show the reader how to apply stochastic processes. Furthermore, Stochastic Processes gives a simple introduction to other stochastic processes such as the cumulative process, the Wiener process, the Brownian motion and reliability applications. Stochastic Processes is suitable for use as a reliability textbook by advanced undergraduate and graduate students. It is also of interest to researchers, engineers and managers who study or practise reliability and maintenance.

Author : Alessandro Birolini
Publisher : Springer Science & Business Media
Page : 113 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642465536

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On the Use of Stochastic Processes in Modeling Reliability Problems by Alessandro Birolini Pdf

Stochastic processes are powerful tools for the investigation of reliability and availability of repairable equipment and systems. Because of the involved models, and in order to be mathematically tractable, these processes are generally confined to the class of regenerative stochastic processes with a finite state space, to which belong: renewal processes, Markov processes, semi-Markov processes, and more general regenerative processes with only one (or a few) regeneration staters). The object of this monograph is to review these processes and to use them in solving some reliability problems encountered in practical applications. Emphasis is given to a comprehensive exposition of the analytical procedures, to the limitations in volved, and to the unification and extension of. the models known in the literature. The models investigated here assume. that systems have only one repair crew and that no further failure can occur at system down. Repair and failure rates are general ized step-by-step, up to the case in which the involved process is regenerative with only one (or a few) regeneration state(s). Investigations deal with different kinds of reliabilities and availabilities for series/parallel structures. Preventive main tenance and imperfect switching are considered in some examples.

Author : Oliver Ibe
Publisher : Newnes
Page : 514 pages
File Size : 47,7 Mb
Release : 2013-05-22
Category : Mathematics
ISBN : 9780124078390

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Markov Processes for Stochastic Modeling by Oliver Ibe Pdf

Markov processes are processes that have limited memory. In particular, their dependence on the past is only through the previous state. They are used to model the behavior of many systems including communications systems, transportation networks, image segmentation and analysis, biological systems and DNA sequence analysis, random atomic motion and diffusion in physics, social mobility, population studies, epidemiology, animal and insect migration, queueing systems, resource management, dams, financial engineering, actuarial science, and decision systems. Covering a wide range of areas of application of Markov processes, this second edition is revised to highlight the most important aspects as well as the most recent trends and applications of Markov processes. The author spent over 16 years in the industry before returning to academia, and he has applied many of the principles covered in this book in multiple research projects. Therefore, this is an applications-oriented book that also includes enough theory to provide a solid ground in the subject for the reader. Presents both the theory and applications of the different aspects of Markov processes Includes numerous solved examples as well as detailed diagrams that make it easier to understand the principle being presented Discusses different applications of hidden Markov models, such as DNA sequence analysis and speech analysis.

Author : Limnios
Publisher : Wiley-Blackwell
Page : 128 pages
File Size : 48,7 Mb
Release : 2016-08-17
Category : Electronic
ISBN : 1848218907

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Estimation of Reliability of Repairable Semi-Markov Systems with Finite State Space by Limnios Pdf

Author : Vlad Stefan Barbu,Nicolas Vergne
Publisher : John Wiley & Sons
Page : 288 pages
File Size : 46,9 Mb
Release : 2020-12-03
Category : Mathematics
ISBN : 9781786306036

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Statistical Topics and Stochastic Models for Dependent Data with Applications by Vlad Stefan Barbu,Nicolas Vergne Pdf

This book is a collective volume authored by leading scientists in the field of stochastic modelling, associated statistical topics and corresponding applications. The main classes of stochastic processes for dependent data investigated throughout this book are Markov, semi-Markov, autoregressive and piecewise deterministic Markov models. The material is divided into three parts corresponding to: (i) Markov and semi-Markov processes, (ii) autoregressive processes and (iii) techniques based on divergence measures and entropies. A special attention is payed to applications in reliability, survival analysis and related fields.

Author : Attila Csenki
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461226741

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Dependability for Systems with a Partitioned State Space by Attila Csenki Pdf

Probabilistic models of technical systems are studied here whose finite state space is partitioned into two or more subsets. The systems considered are such that each of those subsets of the state space will correspond to a certain performance level of the system. The crudest approach differentiates between 'working' and 'failed' system states only. Another, more sophisticated, approach will differentiate between the various levels of redundancy provided by the system. The dependability characteristics examined here are random variables associated with the state space's partitioned structure; some typical ones are as follows • The sequence of the lengths of the system's working periods; • The sequences of the times spent by the system at the various performance levels; • The cumulative time spent by the system in the set of working states during the first m working periods; • The total cumulative 'up' time of the system until final breakdown; • The number of repair events during a fmite time interval; • The number of repair events until final system breakdown; • Any combination of the above. These dependability characteristics will be discussed within the Markov and semi-Markov frameworks.

Author : Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca
Publisher : John Wiley & Sons
Page : 316 pages
File Size : 49,6 Mb
Release : 2017-05-24
Category : Mathematics
ISBN : 9781119415114

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Semi-Markov Migration Models for Credit Risk by Guglielmo D'Amico,Giuseppe Di Biase,Jacques Janssen,Raimondo Manca Pdf

Credit risk is one of the most important contemporary problems for banks and insurance companies. Indeed, for banks, more than forty percent of the equities are necessary to cover this risk. Though this problem is studied by large rating agencies with substantial economic, social and financial tools, building stochastic models is nevertheless necessary to complete this descriptive orientation. This book presents a complete presentation of such a category of models using homogeneous and non-homogeneous semi-Markov processes developed by the authors in several recent papers. This approach provides a good method of evaluating the default risk and the classical VaR indicators used for Solvency II and Basel III governance rules. This book is the first to present a complete semi-Markov treatment of credit risk while also insisting on the practical use of the models presented here, including numerical aspects, so that this book is not only useful for scientific research but also to managers working in this field for banks, insurance companies, pension funds and other financial institutions.