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Markov Chains And Dependability Theory

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Markov Chains And Dependability Theory

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Author : Gerardo Rubino
language : en
Publisher:
Release Date : 2014-06-12

Markov Chains And Dependability Theory written by Gerardo Rubino and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Electronic books categories.

Covers fundamental and applied results of Markov chain analysis for the evaluation of dependability metrics, for graduate students and researchers.

Dependability For Systems With A Partitioned State Space

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Author : Attila Csenki
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Dependability For Systems With A Partitioned State Space written by Attila Csenki and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Markov Chains And Dependability Theory

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Author : Gerardo Rubino
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-12

Markov Chains And Dependability Theory written by Gerardo Rubino and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Business & Economics categories.

Covers fundamental and applied results of Markov chain analysis for the evaluation of dependability metrics, for graduate students and researchers.

Semi Markov Processes And Reliability

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Author : Nikolaos Limnios
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-02-16

Semi Markov Processes And Reliability written by Nikolaos Limnios and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-16 with Technology & Engineering categories.

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.

Markov Chains

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Author : Bruno Sericola
language : en
Publisher: John Wiley & Sons
Release Date : 2013-08-05

Markov Chains written by Bruno Sericola and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-05 with Mathematics categories.

Markov chains are a fundamental class of stochastic processes. They are widely used to solve problems in a large number of domains such as operational research, computer science, communication networks and manufacturing systems. The success of Markov chains is mainly due to their simplicity of use, the large number of available theoretical results and the quality of algorithms developed for the numerical evaluation of many metrics of interest. The author presents the theory of both discrete-time and continuous-time homogeneous Markov chains. He carefully examines the explosion phenomenon, the Kolmogorov equations, the convergence to equilibrium and the passage time distributions to a state and to a subset of states. These results are applied to birth-and-death processes. He then proposes a detailed study of the uniformization technique by means of Banach algebra. This technique is used for the transient analysis of several queuing systems. Contents 1. Discrete-Time Markov Chains 2. Continuous-Time Markov Chains 3. Birth-and-Death Processes 4. Uniformization 5. Queues About the Authors Bruno Sericola is a Senior Research Scientist at Inria Rennes – Bretagne Atlantique in France. His main research activity is in performance evaluation of computer and communication systems, dependability analysis of fault-tolerant systems and stochastic models.

Recent Advances In Reliability Theory

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Author : Nikolaos Limnios
language : en
Publisher: Springer Science & Business Media
Release Date : 2000

Recent Advances In Reliability Theory written by Nikolaos Limnios and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

1 Reliability: Past, Present, Future.- 2 Reliability Analysis as a Tool for Expressing and Communicating Uncertainty.- 3 Modeling a Process of Non-Ideal Repair.- 4 Some Models and Mathematical Results for Reliability of Systems of Components.- 5 Algorithms of Stochastic Activity and Problems of Reliability.- 6 Some Shifted Stochastic Orders.- 7 Characterization of Distributions in Reliability.- 8 Asymptotic Analysis of Reliability for Switching Systems in Light and Heavy Traffic Conditions.- 9 Nonlinearly Perturbed Markov Chains and Large Deviations for Lifetime Functionals.- 10 Evolutionary Systems in an Asymptotic Split Phase Space.- 11 An Asymptotic Approach to Multistate Systems Reliability Evaluation.- 12 Computer Intensive Methods Based on Resampling in Analysis of Reliability and Survival Data.- 13 Statistical Analysis of Damage Processes.- 14 Data Analysis Based on Warranty Database.- 15 Failure Models Indexed by Time and Usage.- 16 A New Multiple Proof Loads Approach For Estimating Correlations.- 17 Conditional and Partial Correlation For Graphical Uncertainty Models.- 18 Semiparametric Methods of Time Scale Selection.- 19 Censored and Truncated Lifetime Data.- 20 Tests for a Family of Survival Models Based on Extremes.- 21 Software Reliability Models - Past, Present and Future.- 22 Dynamic Analysis of Failures in Repairable Systems and Software.- 23 Precedence Test and Maximal Precedence Test.- 24 Hierarchical Bayesian Inference in Related Reliability Experiments.- 25 Tests for Equality of Intensities of Failures of a Repairable System Under Two Competing Risks.- 26 Semiparametric Estimation in Accelerated Life Testing.- 27 A Theoretical Framework for Accelerated Testing.- 28 Unbiased Estimation in Reliability and Similar Problems.- 29 Prediction Under Association.- 30 Uniform Limit Laws for Kernel Density Estimators on Possibly Unbounded Intervals.- 31 A Weak Convergence Result Relevant in Recurrent and Renewal Models.

Semi Markov Chains And Hidden Semi Markov Models Toward Applications

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Author : Vlad Stefan Barbu
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-01-07

Semi Markov Chains And Hidden Semi Markov Models Toward Applications written by Vlad Stefan Barbu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-07 with Mathematics categories.

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.

Markov Chains

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Author : Bruno Sericola
language : en
Publisher: Wiley-ISTE
Release Date : 2013-07-22

Markov Chains written by Bruno Sericola and has been published by Wiley-ISTE this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-22 with Mathematics categories.

Reliability Theory

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Author : Ilya Gertsbakh
language : en
Publisher: Springer
Release Date : 2013-12-21

Reliability Theory written by Ilya Gertsbakh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Technology & Engineering categories.

The material in this book was first presented as a one-semester course in Relia bility Theory and Preventive Maintenance for M.Sc. students of the Industrial Engineering Department of Ben Gurion University in the 1997/98 and 1998/99 academic years. Engineering students are mainly interested in the applied part of this theory. The value of preventive maintenance theory lies in the possibility of its imple mentation, which crucially depends on how we handle statistical reliability data. The very nature of the object of reliability theory - system lifetime - makes it extremely difficult to collect large amounts of data. The data available are usu ally incomplete, e.g. heavily censored. Thus, the desire to make the course material more applicable led me to include in the course topics such as mod eling system lifetime distributions (Chaps. 1,2) and the maximum likelihood techniques for lifetime data processing (Chap. 3). A course in the theory of statistics is aprerequisite for these lectures. Stan dard courses usually pay very little attention to the techniques needed for our purpose. A short summary of them is given in Chap. 3, including widely used probability plotting. Chapter 4 describes the most useful and popular models of preventive main tenance and replacement. Some practical aspects of applying these models are addressed, such as treating uncertainty in the data, the role of data contamina tion and the opportunistic scheduling of maintenance activities.

Stochastic Processes

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Author : Toshio Nakagawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-27

Stochastic Processes written by Toshio Nakagawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-27 with Technology & Engineering categories.

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.

Markov Chains And Dependability Theory

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