Description: 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 transmissionsystem 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.

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