Mathematical Theory Of Reliability Of Time Dependent Systems With Practical Applications

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Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications

Igor N. Kovalenko,Philip A. Pegg
Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications Book PDF

Author : Igor N. Kovalenko,Philip A. Pegg
Publisher : John Wiley & Sons
Page : 328 pages
File Size : 44,5 Mb
Release : 1997-07-16
Category : Mathematics
ISBN : STANFORD:36105019810675

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Mathematical Theory of Reliability of Time Dependent Systems with Practical Applications by Igor N. Kovalenko,Philip A. Pegg Pdf

One of the greatest problems in engineering is reliability. The performance of all machinery degrades over time and unless counteraction is taken at some point, any system will eventually fail. Once a system fails there are a number of possible solutions; the mathematical and statistical measurement and analysis of these solutions forms the mathematical theory of reliability. The aim of the authors is to concentrate on aspects of particular importance in the mathematical theory of reliability of time dependent systems rather than give a general overview. Particular emphasis is placed on fault tree analysis, Monte Carlo methods and importance measures. This book will be of particular interest to applied researchers and engineers working in areas where reliability is crucial. Contents Introduction, Markov and Semi-Markov models as a basis for the mathematical analysis of system reliability, methods for investigating homogeneous and non-homogeneous point processes (event flows), fault trees ? the current state of research, theory of redundant systems, Monte Carlo methods, reliability analysis using perturbation methods, stiff processes in reliability analysis, variance reduction methods, analytical-statistical methods for rapid simulation of repairable systems with structure redundancy, measures of reliability importance of components, index.

Mathematical Theory of Reliability

Richard E. Barlow,Frank Proschan
Mathematical Theory of Reliability Book PDF

Author : Richard E. Barlow,Frank Proschan
Publisher : SIAM
Page : 271 pages
File Size : 52,6 Mb
Release : 1996-01-01
Category : Technology & Engineering
ISBN : 9780898713695

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Mathematical Theory of Reliability by Richard E. Barlow,Frank Proschan Pdf

This monograph presents a survey of mathematical models useful in solving reliability problems. It includes a detailed discussion of life distributions corresponding to wearout and their use in determining maintenance policies, and covers important topics such as the theory of increasing (decreasing) failure rate distributions, optimum maintenance policies, and the theory of coherent systems. The emphasis throughout the book is on making minimal assumptions - and only those based on plausible physical considerations - so that the resulting mathematical deductions may be safely made about a large variety of commonly occurring reliability situations. The first part of the book is concerned with component reliability, while the second part covers system reliability, including problems that are as important today as they were in the 1960s. The enduring relevance of the subject of reliability and the continuing demand for a graduate-level book on this topic are the driving forces behind its re-publication.

Multi-State System Reliability

Anatoly Lisnianski,Gregory Levitin
Multi State System Reliability Book PDF

Author : Anatoly Lisnianski,Gregory Levitin
Publisher : World Scientific Publishing Company
Page : 376 pages
File Size : 51,9 Mb
Release : 2003-03-12
Category : Mathematics
ISBN : 9789813106147

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Multi-State System Reliability by Anatoly Lisnianski,Gregory Levitin Pdf

Most books on reliability theory are devoted to traditional binary reliability models allowing for only two possible states for a system and its components: perfect functionality and complete failure. However, many real-world systems are composed of multi-state components, which have different performance levels and several failure modes with various effects on the entire system performance (degradation). Such systems are called Multi-State Systems (MSS). The examples of MSS are power systems where the component performance is characterized by the generating capacity, computer systems where the component performance is characterized by the data processing speed, communication systems, etc. This book is the first to be devoted to Multi-State System (MSS) reliability analysis and optimization. It provides a historical overview of the field, presents basic concepts of MSS, defines MSS reliability measures, and systematically describes the tools for MSS reliability assessment and optimization. Basic methods for MSS reliability assessment, such as a Boolean methods extension, basic random process methods (both Markov and semi-Markov) and universal generating function models, are systematically studied. A universal genetic algorithm optimization technique and all details of its application are described. All the methods are illustrated by numerical examples. The book also contains many examples of application of reliability assessment and optimization methods to real engineering problems. The aim of this book is to give a comprehensive, up-to-date presentation of MSS reliability theory based on modern advances in this field and provide a theoretical summary and examples of engineering applications to a variety of technical problems. From this point of view the book bridges the gap between theoretical advances and practical reliability engineering.

Nonlinearly Perturbed Semi-Markov Processes

Dmitrii Silvestrov,Sergei Silvestrov
Nonlinearly Perturbed Semi Markov Processes Book PDF

Author : Dmitrii Silvestrov,Sergei Silvestrov
Publisher : Springer
Page : 143 pages
File Size : 45,7 Mb
Release : 2017-09-06
Category : Mathematics
ISBN : 9783319609881

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Nonlinearly Perturbed Semi-Markov Processes by Dmitrii Silvestrov,Sergei Silvestrov Pdf

The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions. Effective recurrent algorithms are composed for getting asymptotic expansions, without and with explicit upper bounds for remainders, for power moments of hitting times, stationary and conditional quasi-stationary distributions for nonlinearly perturbed semi-Markov processes. These results are illustrated by asymptotic expansions for birth-death-type semi-Markov processes, which play an important role in various applications. The book will be a useful contribution to the continuing intensive studies in the area. It is an essential reference for theoretical and applied researchers in the field of stochastic processes and their applications that will contribute to continuing extensive studies in the area and remain relevant for years to come.

Time Series

Ngai Hang Chan
Time Series Book PDF

Author : Ngai Hang Chan
Publisher : John Wiley & Sons
Page : 225 pages
File Size : 51,9 Mb
Release : 2004-04-05
Category : Mathematics
ISBN : 9780471461647

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Time Series by Ngai Hang Chan Pdf

Elements of Financial Time Series fills a gap in the market in the area of financial time series analysis by giving both conceptual and practical illustrations. Examples and discussions in the later chapters of the book make recent developments in time series more accessible. Examples from finance are maximized as much as possible throughout the book. * Full set of exercises is displayed at the end of each chapter. * First seven chapters cover standard topics in time series at a high-intensity level. * Recent and timely developments in nonstandard time series techniques are illustrated with real finance examples in detail. * Examples are systemically illustrated with S-plus with codes and data available on an associated Web site.

Approximation Theorems of Mathematical Statistics

Robert J. Serfling
Approximation Theorems of Mathematical Statistics Book PDF

Author : Robert J. Serfling
Publisher : John Wiley & Sons
Page : 392 pages
File Size : 46,9 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317198

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Approximation Theorems of Mathematical Statistics by Robert J. Serfling Pdf

Approximation Theorems of Mathematical Statistics This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory. The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of: * The tools and foundations that are basic to asymptotic theory in statistics * The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence * Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding's U-statistics and R. von Mises's "differentiable statistical functions" * Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics") * Use of influence curves * Approaches toward asymptotic relative efficiency of statistical test procedures

Optimization Methods and Applications

Sergiy Butenko,Panos M. Pardalos,Volodymyr Shylo
Optimization Methods and Applications Book PDF

Author : Sergiy Butenko,Panos M. Pardalos,Volodymyr Shylo
Publisher : Springer
Page : 639 pages
File Size : 48,8 Mb
Release : 2018-02-20
Category : Mathematics
ISBN : 9783319686400

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Optimization Methods and Applications by Sergiy Butenko,Panos M. Pardalos,Volodymyr Shylo Pdf

Researchers and practitioners in computer science, optimization, operations research and mathematics will find this book useful as it illustrates optimization models and solution methods in discrete, non-differentiable, stochastic, and nonlinear optimization. Contributions from experts in optimization are showcased in this book showcase a broad range of applications and topics detailed in this volume, including pattern and image recognition, computer vision, robust network design, and process control in nonlinear distributed systems. This book is dedicated to the 80th birthday of Ivan V. Sergienko, who is a member of the National Academy of Sciences (NAS) of Ukraine and the director of the V.M. Glushkov Institute of Cybernetics. His work has had a significant impact on several theoretical and applied aspects of discrete optimization, computational mathematics, systems analysis and mathematical modeling.

Regression Models for Time Series Analysis

Benjamin Kedem,Konstantinos Fokianos
Regression Models for Time Series Analysis Book PDF

Author : Benjamin Kedem,Konstantinos Fokianos
Publisher : John Wiley & Sons
Page : 361 pages
File Size : 48,7 Mb
Release : 2005-03-11
Category : Mathematics
ISBN : 9780471461685

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Regression Models for Time Series Analysis by Benjamin Kedem,Konstantinos Fokianos Pdf

A thorough review of the most current regression methods in time series analysis Regression methods have been an integral part of time series analysis for over a century. Recently, new developments have made major strides in such areas as non-continuous data where a linear model is not appropriate. This book introduces the reader to newer developments and more diverse regression models and methods for time series analysis. Accessible to anyone who is familiar with the basic modern concepts of statistical inference, Regression Models for Time Series Analysis provides a much-needed examination of recent statistical developments. Primary among them is the important class of models known as generalized linear models (GLM) which provides, under some conditions, a unified regression theory suitable for continuous, categorical, and count data. The authors extend GLM methodology systematically to time series where the primary and covariate data are both random and stochastically dependent. They introduce readers to various regression models developed during the last thirty years or so and summarize classical and more recent results concerning state space models. To conclude, they present a Bayesian approach to prediction and interpolation in spatial data adapted to time series that may be short and/or observed irregularly. Real data applications and further results are presented throughout by means of chapter problems and complements. Notably, the book covers: * Important recent developments in Kalman filtering, dynamic GLMs, and state-space modeling * Associated computational issues such as Markov chain, Monte Carlo, and the EM-algorithm * Prediction and interpolation * Stationary processes

The Statistical Analysis of Failure Time Data

John D. Kalbfleisch,Ross L. Prentice
The Statistical Analysis of Failure Time Data Book PDF

Author : John D. Kalbfleisch,Ross L. Prentice
Publisher : John Wiley & Sons
Page : 462 pages
File Size : 55,9 Mb
Release : 2002-09-09
Category : Mathematics
ISBN : 9780471363576

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The Statistical Analysis of Failure Time Data by John D. Kalbfleisch,Ross L. Prentice Pdf

* Contains additional discussion and examples on left truncation as well as material on more general censoring and truncation patterns. * Introduces the martingale and counting process formulation swil lbe in a new chapter. * Develops multivariate failure time data in a separate chapter and extends the material on Markov and semi Markov formulations. * Presents new examples and applications of data analysis.

Analysis of Financial Time Series

Ruey S. Tsay
Analysis of Financial Time Series Book PDF

Author : Ruey S. Tsay
Publisher : John Wiley & Sons
Page : 724 pages
File Size : 54,6 Mb
Release : 2010-08-30
Category : Mathematics
ISBN : 9780470414354

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Analysis of Financial Time Series by Ruey S. Tsay Pdf

This book provides a broad, mature, and systematic introduction to current financial econometric models and their applications to modeling and prediction of financial time series data. It utilizes real-world examples and real financial data throughout the book to apply the models and methods described. The author begins with basic characteristics of financial time series data before covering three main topics: Analysis and application of univariate financial time series The return series of multiple assets Bayesian inference in finance methods Key features of the new edition include additional coverage of modern day topics such as arbitrage, pair trading, realized volatility, and credit risk modeling; a smooth transition from S-Plus to R; and expanded empirical financial data sets. The overall objective of the book is to provide some knowledge of financial time series, introduce some statistical tools useful for analyzing these series and gain experience in financial applications of various econometric methods.

Runs and Scans with Applications

Narayanaswamy Balakrishnan,Markos V. Koutras
Runs and Scans with Applications Book PDF

Author : Narayanaswamy Balakrishnan,Markos V. Koutras
Publisher : John Wiley & Sons
Page : 484 pages
File Size : 41,6 Mb
Release : 2011-09-20
Category : Mathematics
ISBN : 9781118150450

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Runs and Scans with Applications by Narayanaswamy Balakrishnan,Markos V. Koutras Pdf

Expert practical and theoretical coverage of runs and scans This volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems. The authors provide detailed discussions of both classical and current problems, such as: * Sooner and later waiting time * Consecutive systems * Start-up demonstration testing in life-testing experiments * Learning and memory models * "Match" in genetic codes Runs and Scans with Applications offers broad coverage of the subject in the context of reliability and life-testing settings and serves as an authoritative reference for students and professionals alike.

Linear Statistical Inference and its Applications

C. Radhakrishna Rao
Linear Statistical Inference and its Applications Book PDF

Author : C. Radhakrishna Rao
Publisher : John Wiley & Sons
Page : 656 pages
File Size : 42,9 Mb
Release : 2009-09-25
Category : Mathematics
ISBN : 9780470317143

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Linear Statistical Inference and its Applications by C. Radhakrishna Rao Pdf

"C. R. Rao would be found in almost any statistician's list of five outstanding workers in the world of Mathematical Statistics today. His book represents a comprehensive account of the main body of results that comprise modern statistical theory." -W. G. Cochran "[C. R. Rao is] one of the pioneers who laid the foundations of statistics which grew from ad hoc origins into a firmly grounded mathematical science." -B. Efrom Translated into six major languages of the world, C. R. Rao's Linear Statistical Inference and Its Applications is one of the foremost works in statistical inference in the literature. Incorporating the important developments in the subject that have taken place in the last three decades, this paperback reprint of his classic work on statistical inference remains highly applicable to statistical analysis. Presenting the theory and techniques of statistical inference in a logically integrated and practical form, it covers: * The algebra of vectors and matrices * Probability theory, tools, and techniques * Continuous probability models * The theory of least squares and the analysis of variance * Criteria and methods of estimation * Large sample theory and methods * The theory of statistical inference * Multivariate normal distribution Written for the student and professional with a basic knowledge of statistics, this practical paperback edition gives this industry standard new life as a key resource for practicing statisticians and statisticians-in-training.

Methods and Applications of Linear Models

Ronald R. Hocking
Methods and Applications of Linear Models Book PDF

Author : Ronald R. Hocking
Publisher : John Wiley & Sons
Page : 773 pages
File Size : 45,9 Mb
Release : 2005-02-04
Category : Mathematics
ISBN : 9780471458623

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Methods and Applications of Linear Models by Ronald R. Hocking Pdf

A popular statistical text now updated and better than ever! The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved. Now in its second edition, Methods and Applications of Linear Models: Regression and the Analysis of Variance seeks to more effectively address the analysis of such models through several important changes. Notable in this new edition: Fully updated and expanded text reflects the most recent developments in the AVE method Rearranged and reorganized discussions of application and theory enhance text’s effectiveness as a teaching tool More than 100 new exercises in the areas of regression and analysis of variance As in the First Edition, the author presents a thorough treatment of the concepts and methods of linear model analysis, and illustrates them with various numerical and conceptual examples, using a data-based approach to development and analysis. Data sets, available on an FTP site, allow readers to apply analytical methods discussed in the book.

Reliability and Maintenance of Complex Systems

Süleyman Özekici
Reliability and Maintenance of Complex Systems Book PDF

Author : Süleyman Özekici
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 47,5 Mb
Release : 2013-06-29
Category : Computers
ISBN : 9783662032749

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Reliability and Maintenance of Complex Systems by Süleyman Özekici Pdf

Complex high-technology devices are in growing use in industry, service sectors, and everyday life. Their reliability and maintenance is of utmost importance in view of their cost and critical functions. This book focuses on this theme and is intended to serve as a graduate-level textbook and reference book for scientists and academics in the field. The chapters are grouped into five complementary parts that cover the most important aspects of reliability and maintenance: stochastic models of reliability and maintenance, decision models involving optimal replacement and repair, stochastic methods in software engineering, computational methods and simulation, and maintenance management systems. This wide range of topics provides the reader with a complete picture in a self-contained volume.

Nonparametric Analysis of Univariate Heavy-Tailed Data

Natalia Markovich
Nonparametric Analysis of Univariate Heavy Tailed Data Book PDF

Author : Natalia Markovich
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 46,6 Mb
Release : 2008-03-11
Category : Mathematics
ISBN : 0470723599

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Nonparametric Analysis of Univariate Heavy-Tailed Data by Natalia Markovich Pdf

Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution. The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function. Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.