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    Dependability of Engineering Systems: A Markov Minimal Cut Approach

    Hans-Dieter Kochs|2020.04.09

    Content

    Preface

    List of figures

    List of tables

    List of symbols and abbreviations

    1 Example 1: Reference example

    1.1 Mathematical foundation for the integration of Markov minimal

    cuts (MMC)

    1.2 Precise modeling of the MMC and the system up and down

    state

    1.3 Precise calculation of the Markov models

    1.4 Approximate modeling of the MMC

    1.5 Approximate calculation of the MMC models with the pMp

    approach

    1.6 Equivalent DBD based on MC

    1.7 Results

    1.8 Extension

    1.9 Remark to deviations - Model accuracy

    1.10 Preliminary research and related terms and methods

    2 Example 2.1 and 2.2: Parallel-to-series structure

    2.1 Example 2.1: Multiple common cause failures (CCF)

    2.1.1 Precise modeling of the MMC and the system up and

    down state

    2.1.2 Approximate modeling of the MMC

    2.1.3 Approximate calculation of the MMC models with the

    pMp approach

    2.1.4 Equivalent DBD based on MC

    2.1.5 Results

    2.2 Example 2.2: Mix of s-dependencies

    2.2.1 Precise modeling of the MMC and the system up and

    down state

    2.2.2 Approximate modeling of the MMC

    2.2.3 Approximate calculation of the MMC models with the

    pMp approach

    2.2.4 Equivalent DBD based on MC

    2.2.5 Results

    Chapter x 6

    17.10.2019

    3 Example 3.1 and 3.2: Series-to-parallel structure

    3.1 Example 3.1: Multiple common cause failures (CCF)

    3.1.1 Precise modeling of the MMC and the system up and

    down state

    3.1.2 Approximate modeling of the MMC

    3.1.3 Approximate calculation of the MMC models with the

    pMp approach

    3.1.4 Equivalent DBD based on MC

    3.1.5 Results

    3.2 Example 3.2: Mix of s-dependencies

    3.2.1 Precise modeling of the MMC and the system up and

    down state

    3.2.2 Approximate modeling of the MMC

    3.2.3 Approximate calculation of the MMC models with the

    pMp approach

    3.2.4 Equivalent DBD based on MC

    3.2.5 Results

    4 Example 4: 4-out-of-4 (4oo4)

    4.1 Precise modeling of the MMC and the system up and down

    state

    4.2 Approximate modeling of the MMC

    4.3 Approximate calculation of the MMC models with the pMp

    approach

    4.4 Equivalent DBD based on MC

    4.5 Results

    5 Example 5: 3-out-of-4 (3oo4)

    5.1 Precise modeling of the MMC and the system up and down

    state

    5.2 Approximate modeling of the MMC

    5.3 Approximate calculation of the MMC models with the pMp

    approach

    5.4 Equivalent DBD based on MC

    5.5 Results

    6 Example 6.1 and 6.2: 2-out-of-4 (2oo4)

    6.1 Example 6.1: Multiple common cause failures (CCF)

    6.1.1 Precise modeling of the MMC and the system up and

    down state

    6.1.2 Approximate modeling of the MMC

    Chapter x 7

    17.10.2019

    6.1.3 Approximate calculation of the MMC models with the

    pMp approach

    6.1.4 Equivalent DBD based on MC

    6.1.5 Results

    6.2 Example 6.2: Mix of s-dependencies

    6.2.1 Precise modeling of the MMC and the system up and

    down state

    6.2.2 Approximate modeling of the MMC

    6.2.3 Approximate calculation of the MMC models with the

    pMp approach

    6.2.4 Equivalent DBD based on MC

    6.2.5 Results

    7 Example 7: 1-out-of-4 (1oo4)

    7.1 Precise modeling of the MMC and the system up and down

    state

    7.2 Approximate calculation of the MMC models with the pMp

    approach

    7.3 Equivalent DBD based on MC

    7.4 Results

    8 Conclusion and overall assessment

    9 Appendix

    Appendix 9.1

    Appendix 9.2

    Appendix 9.3

    Appendix 9.4

    Appendix 9.5

    Appendix 9.6

    Appendix 9.7

    10 Reference

     

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