Space Fault Tree Theory and System Reliability Analysis

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    The significance of the existence of the system is to realize its function and maintain its stability, that is, the reliability and stability of the reliability. Reliability is affected by factors, component properties and system structure, and its changes are complex. In order to solve this problem, the authors proposed the space fault tree theory in 2012. This book is the first time that the fundamental part of the theory has been presented internationally. The authors of the book are Pro. Tiejun Cui and Dr. Shasha Li.

    Tiejun CUI was born in Shenyang, Liaoning, China in 1983. He received a Ph.D. degree in safety technology and engineering from Liaoning Technical University, China in 2015, and received two postdoctoral degrees. His research interests include safety system engineering, system reliability and system fault evolution processes. He is the author of several books and author and co-author of several publications in international journals, including papers that are indexed by SCI and EI.

    Shasha LI was born in Panjin, Liaoning, China, in 1988. She received a Ph.D. degree in safety management engineering from Liaoning Technical University, China in 2018. Her research interests include safety management engineering and system reliability. She is the author and co-author of several publications in International journals and Chinese journals and books, including papers that are indexed by SCI and EI.


    Content Summary


    1.1 Purpose and Significance 
    1.2 Summary of Research and Problems 
    1.2.1 Fault Tree Research
    1.2.2 Multi-factor Influence and Fault Big Data
    1.2.3 System Function Structure Analysis and Factor Space
    1.2.4 System Reliability and Influencing Factors
    1.2.5 Cloud Model and Similarity
    1.2.6 Object Classification and Similarity 
    1.3 Deficiency of System Reliability 


    Continuous Space Fault Tree
    2.1 Concepts of CSFT
    2.2 Fault Probability Distribution
    2.2.1 Component Fault Probability Distribution 
    2.2.2 System Fault Probability Distribution
    2.3 Importance Distributions
    2.3.1 Probability Importance Distribution
    2.3.2 Criticality Importance Distribution
    2.4 System Fault Probability Distribution Trend
    2.5 Calculation of MTLa
    2.6 Conclusions


    Discrete Space Fault Tree
    3.1 Discrete Space Fault Tree 
    3.2 Significance of DSFT Modified Using Fuzzy Structured Element 
    3.3 Factor Projection Fitting Method
    3.4 Constructions and Applications of EDSFT 
    3.4.1 E-Characteristic Function
    3.4.2 E-Component Fault Probability Distribution 
    3.4.3 E-System Fault Probability Distribution 
    3.4.4 E-Probability Importance Distribution 
    3.4.5 E-Criticality Importance Distribution 
    3.4.6 E-System Fault Probability Distribution Trend
    3.4.7 E-Component Domain Importance 
    3.4.8 E-Factor Importance Distribution
    3.4.9 E-Factor Joint Importance Distribution 
    3.5 Conclusions


    Inward Analysis of System Factor Structure
    4.1 Inward Analysis of System Factor Structure
    4.2 Human–Machine Cognition
    4.3 Table Method
    4.4 Classification Reasoning Method
    4.5 Mathematical Description of Classification Reasoning Method 
    4.6 Item-By-Item Analyses
    4.7 Mathematical Description of Item-by-Item Analyses
    4.8 Conclusions


    Function Structure Analysis and Factor Space
    5.1 Factor Analysis Method of Function Structure
    5.1.1 Factors and Dimension Variability
    5.1.2 Function Structure Analysis Space
    5.2 Factor Logic Description of Function Structure 
    5.2.1 Axiom System of Function Structure Analysis
    5.2.2 Minimization Method of System Function Structure
    5.3 Analysis of System Function Structure
    5.3.1 Analysis with Incomplete Information
    5.3.2 Analysis with Complete Information
    5.4 Conclusions


    System Reliability with Influencing Factors
    6.1 Methodology of Concepts and Definitions
    6.2 Analysis of Relationship between Reliability and Influencing Factors 
    6.2.1 Random Variable Decomposition Formula 
    6.2.2 Causal Relationship Reasoning
    6.2.3 Causal Concept Extraction 
    6.2.4 Background Relationship Analysis
    6.2.5 Factor Dimension Reduction
    6.2.6 Compression of Fault Probability Distribution
    6.3 Algorithm Application 
    6.3.1 Random Variable Decomposition Formula 
    6.3.2 Causal Relationship Reasoning 
    6.3.3 Causal Concept Extraction 
    6.3.4 Background Relationship Analysis
    6.3.5 Factor Dimension Reduction
    6.3.6 Compression of Fault Probability Distribution
    6.4 Conclusions


    Cloudization Space Fault Tree 
    7.1 Definitions of SFT
    7.2 Construction of Cloudization Space Fault Tree
    7.2.1 Basis of CLSFT 
    7.2.2 Cloudization Fault Probability Distribution 
    7.2.3 Cloudization Fault Probability Distribution Trend 
    7.2.4 Cloudization Importance Distribution Probability and Criticality
    7.2.5 Cloudization Factor Importance and Joint Importance Distribution
    7.2.6 Cloudization Component Domain Importance 
    7.2.7 Cloudization Path Set Domain and Cut Set Domain
    7.2.8 Uncertainty Analysis of Reliability Data
    7.3 Example Analysis
    7.3.1 Cloudization Fault Probability Distribution 
    7.3.2 Cloudization Fault Probability Distribution Trend
    7.3.3 Cloudization Importance Distribution Probability and Criticality
    7.3.4 Cloudization Importance Distribution of Factor and Factor Joint 
    7.3.5 Cloudization Component Domain Importance 
    7.3.6 Cloudization Path Set Domain and Cut Set Domain 
    7.3.7 Uncertainty Analysis of Reliability Data 


    Cloud Similarity 
    8.1 Similarity Algorithms of Cloud Model
    8.2 Cloud Similarity Computation Based on Envelope 
    8.3 Algorithm Application 
    8.4 Analyses of Algorithm Advantage
    8.5 Conclusions


    Clustering Analysis and Similarity 
    9.1 Preliminary Knowledge
    9.2 Concepts and Properties of Attribute Circle 
    9.3 Object Clustering Analysis Method 
    9.4 Improvements of Clustering Analysis 
    9.5 Example Analyses 
    9.6 Conclusions

    CHAPTER 10

    Development and Future Prospects 
    10.1 Summary of Space Fault Tree 
    10.2 Future Development of Space Fault Tree

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