Author | Csenki, Attila. author |
---|---|
Title | Dependability for Systems with a Partitioned State Space [electronic resource] : Markov and Semi-Markov Theory and Computational Implementation / by Attila Csenki |
Imprint | New York, NY : Springer New York, 1994 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2674-1 |
Descript | IX, 244 p. online resource |
1 Stochastic processes for dependability assessment -- 1.1 Markov and semi-Markov processes for dependability assessment -- 1.2 Example systems -- 2 Sojourn times for discrete-parameter Markov chains -- 2.1 Distribution theory for sojourn times and related variables -- 2.2 An application: the sequence of repair events for a three-unit power transmission model -- 3 The number of visits until absorption to subsets of the state space by a discrete-parameter Markov chain: the multivariate case -- 3.1 The probability generating function of M and the probability mass function of L -- 3.2 Further results for n ? {2, 3} -- 3.3 Tabular summary of results in Sections 3.1 and 3.2 -- 3.4 A power transmission reliabilty application -- 4 Sojourn times for continuous-parameter Markov chains -- 4.1 Distribution theory for sojourn times -- 4.2 Some further distribution results related to sojourn times -- 4.3 Tabular summary of results in Sections 4.1 and 4.2 -- 4.4 An application: further dependability characteristics of the three-unit power transmission model -- 5 The number of visits to a subset of the state space by a continuous-parameter irreducible Markov chain during a finite time interval -- 5.1 The variable $${M_{{A_1}}}(t)$$ -- 5.2 An application: the number of repairs of a two-unit power transmission system during a finite time interval -- 6 A compound measure of dependability for continuous-time Markov models of repairable systems -- 6.1 The dependability measure and its evaluation by randomization -- 6.2 The evaluation of ?(k, i, n) -- 6.3 Application and computational experience -- 7 A compound measure of dependability for continuous-time absorbing Markov systems -- 7.1 The dependability measure -- 7.2 Proof of Theorem 7.1 -- 7.3 Application: the Markov model of the three-unit power transmission system revisited -- 8 Sojourn times for finite semi-Markov processes -- 8.1 A recurrence relation for the Laplace transform of the vector of sojourn times -- 8.2 Laplace transforms of vectors of sojourn times -- 8.3 Proof of Theorem 8.1 -- 9 The number of visits to a subset of the state space by an irreducible semi-Markov process during a finite time interval: moment results -- 9.1 Preliminaries on the moments of $${M_{{A_1}}}(t)$$ -- 9.2 Main result: the Laplace transform of the measures U? -- 9.3 Proof of Theorem 9.2 -- 9.4 Reliability applications -- 10 The number of visits to a subset of the state space by an irreducibe semi-Markov process during a finite time interval: the probability mass function -- 10.1 The Laplace transform of the probability mass function of $${M_{{A_1}}}(t)$$ -- 10.2 Numerical inversion of Laplace transforms using Laguerre polynomials and fast Fourier transform -- 10.3 Reliability applications -- 10.4 Implementation issues -- 11 The number of specific service levels of a repairable semi-Markov system during a finite time interval: joint distributions -- 11.1 A recurrence relation for h(t; m1, m2) in the Laplace transform domain -- 11.2 A computation scheme for the Laplace transforms -- 12 Finite time-horizon sojourn times for finite semi-Markov processes -- 12.1 The double Laplace transform of finite-horizon sojourn times -- 12.2 An application: the alternating renewal process -- Postscript -- References