(Ebook PDF) Fault trees 1st Edition by Nikolaos Limnios 1905209304 9781905209309 Full chapter

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ISBN 10:         1905209304
ISBN 13: 978-1905209309
Author:          Nikolaos Limnios

Fault trees 1st  Table of contents:

Chapter 1: Single-Component Systems

• 1.1 Distribution of Failure and Reliability

  • 1.1.1 Function of Distribution and Density of Failure
  • 1.1.2 Survival Function: Reliability
  • 1.1.3 Hazard Rate
  • 1.1.4 Maintainability
  • 1.1.5 Mean Times
  • 1.1.6 Mean Residual Lifetime
  • 1.1.7 Fundamental Relationships
  • 1.1.8 Some Probability Distributions

• 1.2 Availability of Repairable Systems

  • 1.2.1 Instantaneous Availability
  • 1.2.2 Asymptotic Availability
  • 1.2.3 Mean Availability
  • 1.2.4 Asymptotic Mean Availability

• 1.3 Reliability in Discrete Time

  • 1.3.1 Discrete Distributions
  • 1.3.2 Reliability

• 1.4 Reliability and Maintenance

  • 1.4.1 Periodic Test: Repair Time is Negligible
  • 1.4.2 Periodic Test: Repair Time is Not Negligible
  • 1.4.3 Mean Duration of a Hidden Failure

• 1.5 Reliability Data

Chapter 2: Multi-Component Systems

• 2.1 Structure Function

• 2.2 Modules and Modular Decomposition

• 2.3 Elementary Structure Systems

  • 2.3.1 Series System
  • 2.3.2 Parallel System
  • 2.3.3 System k-out-of-n
  • 2.3.4 Parallel-Series System
  • 2.3.5 Series-Parallel System

• 2.4 Systems with Complex Structure

• 2.5 Probabilistic Study of the Systems

  • 2.5.1 Introduction
  • 2.5.2 Inclusion-Exclusion Method
  • 2.5.3 Disjoint Products
  • 2.5.4 Factorization
  • 2.5.5 Reliability Bounds

Chapter 3: Construction of Fault Trees

• 3.1 Basic Ideas and Definitions

  • 3.1.1 Graphic Symbols
  • 3.1.2 Use of the Operators

• 3.2 Formal Definition and Graphs

• 3.3 Stages of Construction

  • 3.3.1 Preliminary Analysis
  • 3.3.2 Specifications
  • 3.3.3 Construction

• 3.4 Example of Construction

  • 3.4.1 Preliminary Analysis
  • 3.4.2 Specifications
  • 3.4.3 Construction

• 3.5 Automatic Construction

Chapter 4: Minimal Sets

• 4.1 Introduction

• 4.2 Methods of Study

  • 4.2.1 Direct Methods
  • 4.2.2 Descending Methods
  • 4.2.3 Ascending Methods

• 4.3 Reduction

• 4.4 Other Algorithms for Searching the Cut Sets

• 4.5 Inversion of Minimal Cut Sets

• 4.6 Complexity of the Search for Minimal Cut Sets

Chapter 5: Probabilistic Assessment

• 5.1 The Problem of Assessment

• 5.2 Direct Methods

  • 5.2.1 AND Operator
  • 5.2.2 OR Operator
  • 5.2.3 Exclusive OR Operator
  • 5.2.4 k-out-of-n Operator
  • 5.2.5 Priority-AND Operator
  • 5.2.6 IF Operator

• 5.3 Methods of Minimal Sets

  • 5.3.1 Inclusion-Exclusion Development
  • 5.3.2 Disjoint Products
  • 5.3.3 Kitt Method

• 5.4 Method of Factorization

• 5.5 Direct Recursive Methods

  • 5.5.1 Recursive Inclusion-Exclusion Method
  • 5.5.2 Method of Recursive Disjoint Products

• 5.6 Other Methods for Calculating the Fault Trees

• 5.7 Large Fault Trees

  • 5.7.1 Method of Modarres and Dezfuli
  • 5.7.2 Method of Hughes
  • 5.7.3 Schneeweiss Method
  • 5.7.4 Brown Method

Chapter 6: Influence Assessment

• 6.1 Uncertainty

  • 6.1.1 Introduction
  • 6.1.2 Methods for Evaluating the Uncertainty
  • 6.1.3 Evaluation of the Moments

• 6.2 Importance

  • 6.2.1 Introduction
  • 6.2.2 Structural Importance Factors
  • 6.2.3 Probabilistic Importance Factors
  • 6.2.4 Importance Factors Over the Uncertainty

Chapter 7: Modules – Phases – Common Modes

• 7.1 Introduction

• 7.2 Modular Decomposition of an FT

  • 7.2.1 Module and Better Modular Representation
  • 7.2.2 Modularization of a Fault Tree

• 7.3 Multiphase Fault Trees

  • 7.3.1 Example
  • 7.3.2 Transformation of a Multiphase System
  • 7.3.3 Method of Eliminating the Minimal Cut Sets

• 7.4 Common Mode Failures

Chapter 8: Extensions: Non-Coherent, Delay and Multistate Fault Trees

• 8.1 Non-Coherent Fault Trees

  • 8.1.1 Introduction
  • 8.1.2 An Example of a Non-Coherent FT
  • 8.1.3 Prime Implicants and Implicates
  • 8.1.4 Probabilistic Study

• 8.2 Delay Fault Trees

  • 8.2.1 Introduction
  • 8.2.2 Treatment

• 8.3 FTs and Multistate Systems

  • 8.3.1 Multistate Systems
  • 8.3.2 Structure Function
  • 8.3.3 Stochastic Description and Function of Reliability
  • 8.3.4 Fault Trees with Restrictions
  • 8.3.5 Multistate Fault Trees

Chapter 9: Binary Decision Diagrams

• 9.1 Introduction

• 9.2 Reduction of the Shannon Tree

  • 9.2.1 Graphical Representation of a BDD
  • 9.2.2 Formal BDD
  • 9.2.3 Probabilistic Calculation

• 9.3 Probabilistic Assessment of the FTs Based on the BDD

• 9.4 Research About the Prime Implicants

• 9.5 Algorithmic Complexity

Chapter 10: Stochastic Simulation of Fault Trees

• 10.1 Introduction

• 10.2 Generation of Random Variables

  • 10.2.1 Generation of a Uniform Variable
  • 10.2.2 Generation of Discrete Random Variables
  • 10.2.3 Generation of Real Random Variables

• 10.3 Implementation and Evaluation of the Method

  • 10.3.1 The Monte Carlo Method
  • 10.3.2 Estimating the Probability of the Top Event
  • 10.3.3 Precision of the Estimation
  • 10.3.4 Acceleration of the Convergence
  • 10.3.5 Rare Events

Exercises

Appendices

• A: BDD Algorithms in FT Analysis

  • A1: Introduction
  • A2: Obtaining the BDD
  • A3: Algorithm of Probabilistic Assessment
  • A4: Importance Factors
  • A5: Prime Implicants

• B: European Benchmark Fault Trees

  • B1: Description of the Data
  • B2: Fault Tree: Europe-1
  • B3: Fault Tree: Europe-2
  • B4: Fault Tree: Europe-3

• C: Some Results of Probabilities

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