Format:
Online-Ressource (210p)
,
online resource
Edition:
Springer eBook Collection. Computer Science
ISBN:
9781461302735
Series Statement:
Network Theory and Applications 4
Content:
Since its start in 1980 the study of the consecutive-k system has resulted in the accumulation of hundreds of research papers. Its popularity is due to its close ties with many mathematical topics such that the system has become a prototype of how mathematical analysis can help in the study of system reliability. This is the first book to put together all the material on the subject. However, it is not just a collection of results. The authors have built a framework to fit the results into and then sort them and compare them, so that the reader has a good idea what is currently the best methodology. The authors also cover important extensions such as window systems, network systems, graph systems, and 2-dimensional systems. The consecutive-k system is known for its wide applicability and the authors have included a chapter on applications. Audience: All systems engineering researchers, not just those specializing in the consecutive-k system. The book could also be used for a graduate course to demonstrate how mathematics is actually applied to systems engineering
Note:
1. Introduction1.1 The consecutive system and generalizations -- 1.2 The problems and the methodologies -- 1.3 Notation -- 2. Computation of Reliability -- 2.1 Recursive equations -- 2.2 The matrix approach -- 2.3 The combinatorial approach -- 2.4 Bounds and approximations -- 3. Design of Optimal Consecutive Systems -- 3.1 Optimal consecutive-2 systems -- 3.2 Invariant consecutive-k systems -- 3.3 The Birnbaum importance -- 3.4 Half-line importance -- 3.5 The combinatorial importance and the rare-event importance -- 3.6 Consecutive-k G system -- 4. The Lifetime Distribution -- 4.1 Mean time to failure -- 4.2 Estimation of Parameters -- 4.3 Increasing failure rate preservation -- 4.4 IFR property for k ? 4 -- 5. Asymptotic Analysis -- 5.1 Elementary method -- 5.2 Generating function method -- 5.3 Poisson convergence method -- 5.4 The dependence models -- 5.5 Distribution for exchangeable lifetimes -- 6. Window Systems -- 6.1 The k-within-consecutive-m-out- of-n system -- 6.2 The (2, m, n) system -- 6.3 b-Fold-window systems -- 6.4 Asymptotic analysis -- 7. The Network Model -- 7.1 The linear consecutive-2 network system -- 7.2 Connectivity and hamiltonian reliability -- 7.3 The reversible model -- 7.4 The k ? 3 case -- 8. Consecutive-2 Graphs -- 8.1 Reliabilities of consecutive-2 graphs -- 8.2 Optimal consecutive-2 graphs: general theory -- 8.3 Invariant d-nary trees -- 8.4 Other consecutive-2 graphs -- 8.5 The 2-dimensional case -- 9. Some Related Systems -- 9.1 Consecutively connected systems -- 9.2 Multi-failure consecutive systems -- 9.3 Redundant consecutive-k systems -- 9.4 Weighted consecutive systems -- 10. Applications -- 10.1 Examples of modelings -- 10.2 Application examples with computations -- References.
Additional Edition:
ISBN 9781461379720
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781461379720
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780792366614
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9781461302742
Language:
English
DOI:
10.1007/978-1-4613-0273-5
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
