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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

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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