Dependability of Engineering Systems: A Markov Minimal Cut Approach

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