Description: 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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