Dependability of Engineering Systems: A Markov Minimal Cut Approach

ContentPrefaceList of figuresList of tablesList of symbols and abbreviations1 Example 1: Reference example1.1 Mathematical foundation for the integration of Markov minimalcuts (MMC)1.2 Precise modeling of the MMC and the system up and downstate1.3 Precise calculation of the Markov models1.4 Approximate modeling of the MMC1.5 Approximate calculation of the MMC models with the pMpapproach1.6 Equivalent DBD based on MC1.7 Results1.8 Extension1.9 Remark to deviations - Model accuracy1.10 Preliminary research and related terms and methods2 Example 2.1 and 2.2: Parallel-to-series structure2.1 Example 2.1: Multiple common cause failures (CCF)2.1.1 Precise modeling of the MMC and the system up anddown state2.1.2 Approximate modeling of the MMC2.1.3 Approximate calculation of the MMC models with thepMp approach2.1.4 Equivalent DBD based on MC2.1.5 Results2.2 Example 2.2: Mix of s-dependencies2.2.1 Precise modeling of the MMC and the system up anddown state2.2.2 Approximate modeling of the MMC2.2.3 Approximate calculation of the MMC models with thepMp approach2.2.4 Equivalent DBD based on MC2.2.5 ResultsChapter x 617.10.20193 Example 3.1 and 3.2: Series-to-parallel structure3.1 Example 3.1: Multiple common cause failures (CCF)3.1.1 Precise modeling of the MMC and the system up anddown state3.1.2 Approximate modeling of the MMC3.1.3 Approximate calculation of the MMC models with thepMp approach3.1.4 Equivalent DBD based on MC3.1.5 Results3.2 Example 3.2: Mix of s-dependencies3.2.1 Precise modeling of the MMC and the system up anddown state3.2.2 Approximate modeling of the MMC3.2.3 Approximate calculation of the MMC models with thepMp approach3.2.4 Equivalent DBD based on MC3.2.5 Results4 Example 4: 4-out-of-4 (4oo4)4.1 Precise modeling of the MMC and the system up and downstate4.2 Approximate modeling of the MMC4.3 Approximate calculation of the MMC models with the pMpapproach4.4 Equivalent DBD based on MC4.5 Results5 Example 5: 3-out-of-4 (3oo4)5.1 Precise modeling of the MMC and the system up and downstate5.2 Approximate modeling of the MMC5.3 Approximate calculation of the MMC models with the pMpapproach5.4 Equivalent DBD based on MC5.5 Results6 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 anddown state6.1.2 Approximate modeling of the MMCChapter x 717.10.20196.1.3 Approximate calculation of the MMC models with thepMp approach6.1.4 Equivalent DBD based on MC6.1.5 Results6.2 Example 6.2: Mix of s-dependencies6.2.1 Precise modeling of the MMC and the system up anddown state6.2.2 Approximate modeling of the MMC6.2.3 Approximate calculation of the MMC models with thepMp approach6.2.4 Equivalent DBD based on MC6.2.5 Results7 Example 7: 1-out-of-4 (1oo4)7.1 Precise modeling of the MMC and the system up and downstate7.2 Approximate calculation of the MMC models with the pMpapproach7.3 Equivalent DBD based on MC7.4 Results8 Conclusion and overall assessment9 AppendixAppendix 9.1Appendix 9.2Appendix 9.3Appendix 9.4Appendix 9.5Appendix 9.6Appendix 9.710 Reference