Dependability of Engineering Systems: A Markov Minimal Cut Approach

ISBN-13: 9783030383268 / Angielski / Twarda / 2020 / 166 str.

Hans-Dieter Kochs

Spis treści

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

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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

O autorze

Hans-Dieter Kochs was head of the Chair of Computer Engineering and Information Logistics at the University Duisburg-Essen, Germany. He received a Diploma-Degree in Electrical Engineering (1972) and a Dr.-Ing. Degree (1976) from the Technical University (RWTH) Aachen, Germany. From 1972 to 1979 he was a member of the Institute of Power Systems and Power Economics (IAEW) at the RWTH Aachen (Prof. K.W. Edwin) as a research assistant. From 1979 to 1991 he held leading positions in industry (AEG/Daimler Frankfurt, FAG Kugelfischer Erlangen, and ESWE Wiesbaden, Germany). Since 1991 he has been a full Professor. From 1972 to the present day, he has been engaged in scientific and industrial dependability analyses and studies.

Blurb

This book provides an in-depth understanding of precise and approximate MMC modeling and calculation techniques of engineering systems. The in-depth analysis demonstrates that it is only possible to precisely model and calculate the dependability of systems including s-dependent components with the knowledge of their (total) universe spaces, represented here by Markov spaces. They provide the basis for developing and verifying approximate MMC models. With the mathematical steps described and applied to several examples throughout this text, interested system developers and users can perform dependability analyses themselves. All examples are structured in precisely the same way.