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A comprehensive up-to-date presentation of some of the classical areas of reliability, based on a more advanced probabilistic framework using the modern theory of stochastic processes. This framework allows analysts to formulate general failure models, establish formulae for computing various performance measures, as well as determine how to identify optimal replacement policies in complex situations.
With the growing complexity of engineered systems, reliability hasincreased in importance throughout the twentieth century. Initiallydeveloped to meet practical needs, reliability theory has become anapplied mathematical discipline that permits a priori evaluationsof various reliability indices at the design stages. Theseevaluations help engineers choose an optimal system structure,improve methods of maintenance, and estimate the reliability on thebasis of special testing. Probabilistic Reliability Engineeringfocuses on the creation of mathematical models for solving problemsof system design. Broad and authoritative in its content, Probabilistic ReliabilityEngineering covers all mathematical models associated withprobabilistic methods of reliability analysis, including--unique tothis book--maintenance and cost analysis, as well as many newresults of probabilistic testing. To provide readers with all necessary background material, thistext incorporates a thorough review of the fundamentals ofprobability theory and the theory of stochastic processes. Itoffers clear and detailed treatment of reliability indices, thestructure function, load-strength reliability models, distributionswith monotone intensity functions, repairable systems, the Markovmodels, analysis of performance effectiveness, two-pole networks,optimal redundancy, optimal technical diagnosis, and heuristicmethods in reliability. Throughout the text, an abundance of realworld examples and case studies illustrate and illuminate thetheoretical points under consideration. For engineers in design, operations research, and maintenance, aswell as cost analysts and R&D managers, ProbabilisticReliability Engineering offers the most lucid, comprehensivetreatment of the subject available anywhere. About the editor JAMES A. FALK is Professor and Chairman of the Department ofOperations Research at George Washington University. In addition tohis numerous publications, Dr. Falk has lectured internationally asa Fulbright Lecturer. Of related interest... The reliability-testing "bible" for three generations of EasternEuropean scientists, adapted for Western scientists andengineers... HANDBOOK OF RELIABILITY ENGINEERING Originally published in the USSR, Handbook of ReliabilityEngineering set the standard for the reliability testing oftechnical systems for nearly three generations of appliedscientists and engineers. Authored by a group of prominent Sovietspecialists in reliability, it provides professionals and studentswith a comprehensive reference covering mathematical formulas andtechniques for incorporating reliability into engineering designsand testing procedures. Divided into twenty-four self-containedchapters, the Handbook details reliability fundamentals, examinescommon reliability problems and solutions, provides a collection ofcomputation formulas, and illustrates practical applications. The Handbook's Russian editor and internationally recognized expertIgor A. Ushakov has joined with American engineering professionalsto bring this indispensable resource to English-speaking engineersand scientists. 1994 (0-471-57173-3) 663 pp.
This book contains extended versions of carefully selected and reviewed papers presented at the Third International Conference on Mathematical Methods in Reliability, held in Norway in 2002. It provides an overview of current research activities in reliability theory. The authors are all leading experts in the field. Readership: Graduate students, academics and professionals in probability & statistics, reliability analysis, survival analysis, industrial engineering, software engineering, operations research and applied mathematics research.
This book deals with different modern topics in probability, statistics and operations research. It has been written lucidly in a novel way. Wherever necessary, the theory is explained in great detail, with suitable illustrations. Numerous references are given, so that young researchers who want to start their work in a particular area will benefit immensely from the book.The contributors are distinguished statisticians and operations research experts from all over the world.
Mathematical Methods of Reliability Theory discusses fundamental concepts of probability theory, mathematical statistics, and an exposition of the relationships among the fundamental quantitative characteristics encountered in the theory. The book deals with the set-theoretic approach to reliability theory and the central concepts of set theory to the phenomena. It also presents methods of finding estimates for reliability parameters based on observations and methods of testing reliability hypotheses. Based on mathematical statistics, the book also explains formulation of some selected results. It presents a method that increases the reliability of manufactured articles—redundancy. An important part of product quality control is the standards of acceptance-sampling plans which require simplicity, wide content for flexibility, comprehensive characteristics, and variability. The book also tackles economical and rational methods of sampling inspections, highlighting the need for a correct evaluation of environmental conditions—the factors which predetermine the choice of the inspection method. The book then explains how to estimate the efficiency of the operation of the sampling plan after its selection. The book can be helpful for engineers, mathematicians, economists, or industrial managers, as well as for other professionals who work in the technological, political, research, structural, and physico-chemical areas.
These notes represent our summary of much of the recent research that has been done in recent years on approximations and bounds that have been developed for compound distributions and related quantities which are of interest in insurance and other areas of application in applied probability. The basic technique employed in the derivation of many bounds is induc tive, an approach that is motivated by arguments used by Sparre-Andersen (1957) in connection with a renewal risk model in insurance. This technique is both simple and powerful, and yields quite general results. The bounds themselves are motivated by the classical Lundberg exponential bounds which apply to ruin probabilities, and the connection to compound dis tributions is through the interpretation of the ruin probability as the tail probability of a compound geometric distribution. The initial exponential bounds were given in Willmot and Lin (1994), followed by the nonexpo nential generalization in Willmot (1994). Other related work on approximations for compound distributions and applications to various problems in insurance in particular and applied probability in general is also discussed in subsequent chapters. The results obtained or the arguments employed in these situations are similar to those for the compound distributions, and thus we felt it useful to include them in the notes. In many cases we have included exact results, since these are useful in conjunction with the bounds and approximations developed.
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.