New PDF release: Computational Intelligence in Reliability Engineering New

By Gregory Levitin

ISBN-10: 3540334564

ISBN-13: 9783540334569

ISBN-10: 3540334580

ISBN-13: 9783540334583

ISBN-10: 3540373713

ISBN-13: 9783540373711

This quantity comprises chapters providing functions of alternative metaheuristics (ant colony optimization, nice deluge set of rules, cross-entropy technique and particle swarm optimization) in reliability engineering. it is also chapters dedicated to mobile automata and help vector machines and assorted functions of synthetic neural networks, a strong adaptive process that may be used for studying, prediction and optimization. numerous chapters describe varied elements of obscure reliability and purposes of fuzzy and obscure set concept.

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Additional resources for Computational Intelligence in Reliability Engineering New Metaheuristics Neural and Fuzzy Techniques in Reliability

Example text

Let Λ(Γ) be the collection of all proper partitions of Γ(ς,Ε). The states in Λ(Γ) are ordered by the relation τπσ ⇔ Iτ ⊂ Iσ (that is, σ is obtained by Applications of the Cross-Entropy Method in Reliability 49 merging components of τ). Any state σ in Λ(Γ) has a transition path to the terminal state σω = Γ. Therefore Λ(Γ) is a lattice. We consider now the CP (X(t)) of the network. By restricting the process (X(t)) to Λ(Γ) we obtain another Markov process (Ξ(t)), called the Merge Process (MP) of the network.

Hence, by conditioning on Π we have r = E ⎡⎣ϕ ( X (1) ) ⎤⎦ = ∑ P [ Π = π ] P ⎡⎣ϕ ( X (1) ) = 1 | Π = π ⎤⎦ , π ∈Ξ or r = 1 − r = ∑ P [ Π = π =] P ⎡⎣ϕ ( X (1) = 0 ) | Π = π ⎤⎦ . (4) π ∈Ξ Using the definitions of Si and b(π), we can write the last probability in terms of convolutions of exponential distribution functions. Namely, for any t ≥ 0 we have P ⎡⎣ϕ ( X ( t ) ) = 0 | Π = π ⎤⎦ = P ⎡ S0 + L Sb(π )−1 > t | Π = π ⎤ ⎣ ⎦ { ( ) } = 1 − Conv 1 − exp ⎡⎣ −λ ( Ei ) t ⎤⎦ . 0≤i < b π Let gC (π ) = P ⎡⎣ϕ ( X (1) ) = 0 | Π = π ⎤⎦ , (5) (6) as given in equation (5).

However, in highly reliable networks such as modern communication networks, network failure is very infrequent, and direct simulation – also called crude Monte Carlo (CMC) simulation – of such rare events is computationally expensive. Various techniques have been developed to speed up the estimation procedure. For example, Kumamoto proposed a very simple technique called Dagger Sampling to improve the CMC simulation [20]. P. -P. com © Springer-Verlag Berlin Heidelberg 2007 38 Dirk P. Kroese and Kin-Ping Hui well as bound [13].

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Computational Intelligence in Reliability Engineering New Metaheuristics Neural and Fuzzy Techniques in Reliability by Gregory Levitin


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