## Dependability for systems with a partitioned state space: Markov and semi-Markov theory and computational implementationThis work is concerned with the dependability characteristics of reliability models which have a partitioned state space. In applications these partitions will correspond to various degrees of system performance. Both discrete and continuous time systems are considered as well as Markov and semi-Markov systems. With these models one may develop many dependability characteristics including: the number of working periods during an interval, the number of repair periods until system breakdown, and the total time spent in the set of working states. The author shows how the theory may be applied using numerous examples and with three computing packages: MATLAB, MAPLE, and the NAG Fortran 77 subroutine library. As a result, researchers and practioners concerned with analyzing and modelling the performance of systems, and engineers working on systems dependability will find much of interest here. |

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### Contents

Stochastic processes for dependability assessment | 1 |

Sojourn times for discreteparameter Markov chains | 14 |

The number of visits until absorption to subsets of the state space by | 53 |

Copyright | |

11 other sections not shown

### Common terms and phrases

AA,A AA,Al AA2A AA2Ai aA2T AAlA2 AAlAl absorbing Markov chain AGB ABB AGB ABB"1 abg Apple Macintosh assumed Chapter closed form expression column vector component computation continuous-time Corollary 2.6 cumulative distribution function defined dti dt2 equations Figure finite fix(clock follows given IFAIL initial probability vector input('Enter irreducible joint distribution Laguerre polynomials lamt Laplace transform domain Laplace transform inversion Lemma Macintosh SE/30 MAi(t MAl(t Markov chain Markov model Markov process MATLAB MATLAB implementation matrix exponential MB(to notation number of visits O.OOOODO O.OOOODO obtained parameter partitioned probability generating function probability mass function PROOF OF COROLLARY proof of Theorem Qa,a QA2a QA2Ai random recurrence relation reliability renewal argument repair events right hand side Section semi-Markov processes sojourn space subroutine subsets Table TEMP2 TG(to Theorem 2.1 theory transition probability matrix transition rate matrix values variable WRITE(6 WRITEdO

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