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Dependability for Systems with a Partitioned State Space

Markov and Semi-Markov Theory and Computational Implementation

  • Book
  • © 1994

Overview

Authors:
  1. Attila Csenki

    1. Department of Computer Science and Applied Mathematics, Aston University, Birmingham, Great Britain

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Part of the book series: Lecture Notes in Statistics (LNS, volume 90)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. Stochastic Processes for Dependability Assessment

    • Attila Csenki
    Pages 1-13

  3. Sojourn times for Discrete-Parameter Markov Chains

    • Attila Csenki
    Pages 14-52

  4. The Number of Visits Until Absorption to Subsets of the State Space by a Discrete-Parameter Markov Chain: the Multivariate Case

    • Attila Csenki
    Pages 53-68

  5. Sojourn Times for Continuous-Parameter Markov Chains

    • Attila Csenki
    Pages 69-105

  6. The Number of Visits to a Subset of the State Space by a Continuous-Parameter Irreducible Markov Chain During a Finite Time Interval

    • Attila Csenki
    Pages 106-121

  7. A Compound Measure of Dependability for Continuous-Time Markov Models of Repairable Systems

    • Attila Csenki
    Pages 122-140

  8. A Compound Measure of Dependability For Continuous- Time Absorbing Markov Systems

    • Attila Csenki
    Pages 141-150

  9. Sojourn Times for Finite Semi-Markov Processes

    • Attila Csenki
    Pages 151-166

  10. The Number of Visits to a Subset of the State Space by an Irreducible Semi-Markov Process During a Finite Time Interval: Moment Results

    • Attila Csenki
    Pages 167-178

  11. The Number of Visits to a Subset of the State Space by an Irreducible Semi-Markov Process during a Finite Time Interval: The Probability Mass Function

    • Attila Csenki
    Pages 179-204

  12. The Number of Specific Service Levels of a Repairable Semi-Markov System during a Finite Time Interval: Joint Distributions

    • Attila Csenki
    Pages 205-211

  13. Finite Time-Horizon Sojourn Times for Finite Semi-Markov Processes

    • Attila Csenki
    Pages 212-230

  14. Back Matter

    Pages 235-239
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Keywords

About this book

Probabilistic models of technical systems are studied here whose finite state space is partitioned into two or more subsets. The systems considered are such that each of those subsets of the state space will correspond to a certain performance level of the system. The crudest approach differentiates between 'working' and 'failed' system states only. Another, more sophisticated, approach will differentiate between the various levels of redundancy provided by the system. The dependability characteristics examined here are random variables associated with the state space's partitioned structure; some typical ones are as follows • The sequence of the lengths of the system's working periods; • The sequences of the times spent by the system at the various performance levels; • The cumulative time spent by the system in the set of working states during the first m working periods; • The total cumulative 'up' time of the system until final breakdown; • The number of repair events during a fmite time interval; • The number of repair events until final system breakdown; • Any combination of the above. These dependability characteristics will be discussed within the Markov and semi-Markov frameworks.

Authors and Affiliations

  • Department of Computer Science and Applied Mathematics, Aston University, Birmingham, Great Britain

    Attila Csenki

Bibliographic Information

  • Book Title: Dependability for Systems with a Partitioned State Space

  • Book Subtitle: Markov and Semi-Markov Theory and Computational Implementation

  • Authors: Attila Csenki

  • Series Title: Lecture Notes in Statistics

  • DOI: https://doi.org/10.1007/978-1-4612-2674-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1994

  • Softcover ISBN: 978-0-387-94333-6Published: 28 July 1994

  • eBook ISBN: 978-1-4612-2674-1Published: 06 December 2012

  • Series ISSN: 0930-0325

  • Series E-ISSN: 2197-7186

  • Edition Number: 1

  • Number of Pages: IX, 244

  • Topics: Probability Theory and Stochastic Processes, Computational Mathematics and Numerical Analysis

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