Reliabilities of Consecutive-k Systems
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Reliabilities of Consecutive-k Systems: (4 Network Theory and Applications)

Reliabilities of Consecutive-k Systems: (4 Network Theory and Applications)


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About the Book

Since its start in 1980 the study of the consecutive-k system has resulted in the accumulation of many 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 book presents a comprehensive collection of material on the subject. However, the text 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 book also covers 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.

Table of Contents:
1. Introduction.- 1.1 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.


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Product Details
  • ISBN-13: 9780792366614
  • Publisher: Kluwer Academic Publishers
  • Publisher Imprint: Kluwer Academic Publishers
  • Height: 235 mm
  • No of Pages: 212
  • Returnable: Y
  • Width: 155 mm
  • ISBN-10: 0792366611
  • Publisher Date: 30 Nov 2000
  • Binding: Hardback
  • Language: English
  • Returnable: Y
  • Series Title: 4 Network Theory and Applications


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