Reliability Assessment of Safety and Production Systems: Analysis, Modelling, Calculations and Case Studies (Springer Series in Reliability Engineering)

Preface
Acknowledgments
Contents
Abbreviations and Notations
Part IIntroduction, Background and Overview
1 Introduction
	1.1 Human Enterprises Involve Risks
	1.2 Philosophy to Master the Risks
2 Background
	2.1 A Short Story of Reliability Analysis
		2.1.1 Premises
		2.1.2 The Beginning
		2.1.3 A Step Forward of the Reliability Approach
		2.1.4 Consolidation of the Reliability Approach
		2.1.5 Dissemination in All the Industry Sectors
	2.2 Why, When and How to Implement Reliability Studies
		2.2.1 Why
		2.2.2 When
		2.2.3 How
	2.3 Name for the New Discipline
	2.4 Notion of Risk
		2.4.1 Etymology. Danger Versus Peril, Risk and Hazard
		2.4.2 Safety Versus Risk Management Definitions
		2.4.3 Risk Overview in Industrial Context
	References
3 Reliability Study Overview
	3.1 Overview
	3.2 Goal and System Definition
	3.3 How It Works (Functional Analysis)
	3.4 How It Fails (Dysfunctional Analysis)
		3.4.1 Point About Terminology
		3.4.2 Issue Identification
		3.4.3 System Modelling
		3.4.4 Reliability and Operational Data Selection
		3.4.5 Qualitative Analysis
		3.4.6 Quantitative Analysis
	3.5 Comparisons and Decision
	3.6 Prevention and Risk Mitigation
	References
4 Introduction of Basic Core Concepts
	4.1 Preamble
	4.2 Item Definition
	4.3 States of an Item
		4.3.1 Up and Down States
		4.3.2 Operating and Non-operating States
		4.3.3 Restoration States
		4.3.4 Degraded and Critical States
	4.4 Failure and Fault Concept
		4.4.1 Failure Definition
		4.4.2 Fault Definition
		4.4.3 Failure and Fault Classification
		4.4.4 Failure Cause, Failure Mode
		4.4.5 Common Cause, Common Mode and Single Failures
		4.4.6 Critical Failures and Repairs/Restorations
	4.5 Maintenance Related Concepts
		4.5.1 Maintenance, Restoration and Repair Definitions
		4.5.2 Repairable Versus Repaired Items
	4.6 Acronyms and Operational Concepts
		4.6.1 General Considerations
		4.6.2 MUT and MDT
		4.6.3 MTTF and Related Acronyms
		4.6.4 MTBF
		4.6.5 Maintenance Related Acronyms (MTTR, MRT, MFDT…)
	4.7 Probabilistic Concepts
		4.7.1 Introduction to Random Processes
		4.7.2 Basic Random Process
		4.7.3 (Un)Reliability Versus (Un)Availability
		4.7.4 Failure Distribution and Link with MTTF
		4.7.5 Average and Asymptotic Availability/Unavailability
		4.7.6 Failure Rate and Failure Intensities
		4.7.7 Restoration/Repair Rate
	4.8 Conclusion About the Reliability Concepts
	References
5 Dependent and Common Cause Failures
	5.1 Introduction to Dependent and Common Cause Failures
		5.1.1 Identification of the Problem
		5.1.2 Definition
		5.1.3 Dependency Classifications
	5.2 Examples of CCFs Observed in Real Life
		5.2.1 Examples of Typical Accidents Due to CCFs
		5.2.2 Examples of Typical CCFs Detected from Field Feedback
	5.3 Dependent Failures Identification
	5.4 CCF Data Collection
	5.5 CCF Modelling
		5.5.1 Introduction
		5.5.2 The Beta-Factor Model
		5.5.3 The Shock Model
		5.5.4 Other Modelling Methods
	References
6 Extensions to Production Availability and Functional Safety Analyses
	6.1 From Availability to Efficiency
		6.1.1 Binary Items and Introduction of the Efficiency Concept
		6.1.2 Extension to Multistate Systems
		6.1.3 Generalization of the Efficiency Concept
	6.2 From Conventional Safety to Functional Safety
		6.2.1 Generalities About Protection Layers and Safety Systems
		6.2.2 Classification of Safety Systems and Impact of Faults
		6.2.3 Safety Instrumented Systems
	6.3 Overview of Probabilistic Models
	References
Part IIRisk Identification and Qualitative Analyses
7 The Inductive Approaches
	7.1 Need of the Inductive Approach
	7.2 Objectives of Inductive Methods
	7.3 Overview of the Main Inductive Methods
		7.3.1 Similar Approaches
		7.3.2 Area of Implementation
		7.3.3 Study Team
		7.3.4 Use Within System Life Cycle
	References
8 Preliminary Hazard Analysis (PHA)
	8.1 Description of the Method
		8.1.1 Presentation of the Method
		8.1.2 Purposes of the Method
		8.1.3 PHA Procedure
		8.1.4 Resources for the Method
		8.1.5 Comments
	8.2 Other Related Approaches
		8.2.1 Gross Hazard Analysis
		8.2.2 Chemical Industry
		8.2.3 Preliminary Hazard Analysis with Frequencies
	8.3 Use with Other Methods
	8.4 Worked Example 8.1
	References
9 Hazard and Operability Study (HAZOP)
	9.1 Description of the Method
		9.1.1 Presentation of the Method
		9.1.2 Purposes of the Method
		9.1.3 HAZOP Procedure
		9.1.4 Resources for the Method
		9.1.5 Comments
	9.2 Quantified HAZOP
	9.3 HACCP
	9.4 Worked Example 9.1
	9.5 Use with Other Methods
	References
10 Failure Mode, Effects (and Criticality) Analysis, FME(C)A
	10.1 Description of the Method
		10.1.1 Presentation of the Method
		10.1.2 Purposes of the Method
		10.1.3 FMEA Procedure
		10.1.4 Resources for the Method
		10.1.5 Comments
	10.2 FMEA/FMECA Worksheets
	10.3 FMECA
		10.3.1 Criticality Analysis
		10.3.2 Use of Criticality Matrix
		10.3.3 Use of Risk Priority Number
	10.4 Worked Example 10.1
	10.5 Use with Other Methods
	References
11 Other Inductive Methods
	11.1 Checklists
	11.2 What-If?
	11.3 HAZID
	11.4 Additional Methods
	References
12 Comparison of Inductive Approaches
	12.1 Strengths and Weaknesses of Inductive Approaches
		12.1.1 PHA
		12.1.2 HAZOP
		12.1.3 FMEA/FMECA
		12.1.4 Checklists
		12.1.5 What-If?
		12.1.6 HAZID
	12.2 Synthesis
	References
Part IIIModelling of Static Systems. Boolean Approaches
13 The Family of Boolean Approaches
	Reference
14 Mathematical Framework
	14.1 Notion of Events and Boolean Algebra
	14.2 Bases for Time-Independent Probabilistic Calculations
		14.2.1 Probability of the Disjunction (Union) of Events
		14.2.2 Probability of the Conjunction (Intersection) of Events
	14.3 Introduction to Time-Dependent Calculations
	References
15 Reliability Block Diagrams (RBDs)
	15.1 History and Introduction to Reliability Block Diagrams
	15.2 Graphical Symbols and Basic RBD Structures
	15.3 Building an RBD from Simple Examples
	15.4 Tie and Cut Set Identification
		15.4.1 Electrical Analogy
		15.4.2 Concept of Minimal Cut and Tie Sets
	15.5 RBD Representation by Tie and Cut Sets
	15.6 Associated Exercises
	References
16 Fault Tree Analysis (FTA)
	16.1 History and Introduction to Fault Tree Analysis
	16.2 Graphical Symbols and Basic FT Symbols
	16.3 Building an FT of Simple Examples
	16.4 Cut and Tie Set Identification, FTs Versus Success Trees
	16.5 Associated Exercises
	References
17 Qualitative Analysis from RBDs or FTs
	17.1 Single Failure Criterion and Ranking Cut Sets by Order
	17.2 Identification of Potential Common Cause Failures
	17.3 Associated Exercises
	References
18 Extension to Non-Coherent RBDs and FTs
	18.1 Notion of Non-Coherent Systems
	18.2 Prime Implicants
	References
19 Probabilistic Calculations of Elementary Boolean Models
	19.1 Calculation of Basic Logic Structures
		19.1.1 Series Structures/OR Gates
		19.1.2 Parallel Structures/AND Gates
		19.1.3 Extension to Combinations of Series and Parallel Structures
		19.1.4 NOT, NOR and NAND Logic Gates
	19.2 m out of n (m/n) Structures/Gates
	19.3 Sylvester-Poincaré Formula
	References
20 Semi-Quantitative Analysis from RBDs or FTs
	20.1 Ranking Minimal Cut Sets by Probabilities
	20.2 Link with Sylvester-Poincaré Formula
	20.3 Link with Vesely-Fussell Importance Factor
	20.4 Associated Exercises
	References
21 Probabilistic Calculations for Large Boolean Models
	21.1 Overcoming the Sylvester-Poincaré Shortcomings
		21.1.1 Issue Identification
		21.1.2 A Step Forward to the Solution
		21.1.3 Shannon Decomposition
		21.1.4 Binary Decision Diagrams (BDDs)
		21.1.5 BDDs of RBDs and FTs
	21.2 BDD Calculations
		21.2.1 System Failure and Success Probabilities
		21.2.2 Conditional Probabilities
		21.2.3 Cut and Tie Sets
	21.3 Conclusions on BDDs
	21.4 Associated Exercises
	References
22 Time-Dependent Probabilistic Calculations
	22.1 Introduction of Time and Generalities
	22.2 Availability/Unavailability Calculations
		22.2.1 General Case
		22.2.2 RBD and FT-Driven Markov Processes
	22.3 Average Availability/Unavailability Calculations
		22.3.1 Average Over a Given Interval [0, T]
		22.3.2 Asymptotic Availability or Unavailability
	22.4 Failure Frequency and Derived Parameters
		22.4.1 Average Failure Frequency, Number of Failures and MTBF
		22.4.2 Instantaneous Failure Frequency/Birnbaum Importance Factor
		22.4.3 Combination of Sub-FTs for Unavailability and Frequency Calculations
	22.5 Reliability Calculations
		22.5.1 General Case
		22.5.2 Systems Made of Non-repaired Items
		22.5.3 Systems Made of Repaired Items
	22.6 Dynamic Fault Trees
	22.7 Associated Exercises
	References
23 CCF Modelling with FTs and RBDs
	23.1 Introduction
	23.2 Modelling Tangible CCFs
		23.2.1 Introduction of Tangible CCFs in RBD and FT Models
	23.3 Modelling Non-tangible CCFs
		23.3.1 Beta-Factor Model
		23.3.2 Shock Model
	23.4 Considerations with Regards to Item Repairs
	23.5 Lineage CCFs
	23.6 Use of Minimal Cut Sets
	23.7 Associated Exercises
	References
24 Critical States and Importance Factors
	24.1 Critical and Non-critical States
		24.1.1 Minterms and Exclusive and Inclusive Cofactors
		24.1.2 Critical States
		24.1.3 Non-critical States
		24.1.4 Link Between Critical and Non-critical States
		24.1.5 Graphical Synthesis of the Concepts
	24.2 Importance Factors
		24.2.1 Generalities About Importance Factors
		24.2.2 Vesely-Fussell Importance Factor
		24.2.3 Birnbaum Importance Factor (MIF)
		24.2.4 Lambert Importance Factor (CIF)
		24.2.5 Diagnostic Importance Factor (DIF)
		24.2.6 Risk Achievement Worth (RAW), Risk Reduction Worth (RRW)
		24.2.7 Differential Importance Measure (DIM)
		24.2.8 Barlow-Proschan Importance Factor (BPIF)
		24.2.9 Application and Remarks About Importance Factors
	24.3 Associated Exercise
	References
25 Uncertainty Handling with RBDs and FTs
	25.1 Introduction
	25.2 Principle and Application to Non-correlated Events
	25.3 Application to Correlated Events
	25.4 Considerations About the Pseudo Error Factor
	25.5 Conclusions About Uncertainty Propagation
	25.6 Associated Exercise
	References
26 Sequential Analysis Methods
	26.1 Introduction
	26.2 Cause-Consequence Diagram
		26.2.1 Presentation of the Method
		26.2.2 CCD Procedure
		26.2.3 Graphical Symbols
		26.2.4 Cause-Consequence Diagram Analysis
		26.2.5 Worked Example 26.1
		26.2.6 Strengths and Weaknesses
		26.2.7 Use with Other Methods
	26.3 Event Tree
		26.3.1 Presentation of the Method
		26.3.2 ETA Procedure
		26.3.3 Graphical Symbols
		26.3.4 Event Tree Analysis
		26.3.5 Worked Example 26.2
		26.3.6 Dynamic Event Trees
		26.3.7 Strengths and Weaknesses
		26.3.8 Use with Other Methods
	26.4 Bowtie Method
		26.4.1 Presentation of the Method
		26.4.2 Bowtie Procedure
		26.4.3 Worked Example 26.3
		26.4.4 Strengths and Weaknesses
	26.5 LOPA
		26.5.1 Presentation of the Method
		26.5.2 LOPA Procedure
		26.5.3 Resources for the Method
		26.5.4 Worked Example 26.4
		26.5.5 Strengths and Weaknesses
		26.5.6 Use with Other Methods
	26.6 Comparison of the Sequential Methods and Conclusions
	References
27 Combinations or Links of Boolean Models with Other Techniques
	27.1 Introduction
	27.2 Combination with FMEA/FMECA
	27.3 Combination RBD/FT and Vice Versa
	27.4 Combination with Cause-Consequence, Event Tree or Bowtie Analyses
	27.5 Combination with Markov Processes
	27.6 Combination with Petri Nets
	27.7 Link with Root Cause Analysis
	27.8 Link with Belief Networks
		27.8.1 Principle of Belief Networks
		27.8.2 Description of Belief Networks
		27.8.3 Construction of Belief Networks
		27.8.4 Utilisation of Belief Networks
	References
28 Automated Fault Tree Building
	References
29 Boolean Family Exercises
	29.1 Description of the Overpressure Protection System (OPPS)
	29.2 Reliability Data
	29.3 Description of the Exercises Related to the OPPS
	29.4 Solutions of the Exercises Related to the OPPS
		29.4.1 Exercise 15.1: RBD Building
		29.4.2 Exercise 15.2: Tie Set Identification
		29.4.3 Exercise 16.1: FT Building
		29.4.4 Exercise 16.2: Cut Set Identification
		29.4.5 Exercise 20.1: Semi-quantitative Analysis (Basic)
		29.4.6 Exercise 20.2: Semi-quantitative Analysis with Partial and Full Stroking Tests
		29.4.7 Exercise 20.3: Vesely-Fussell Importance Factor
		29.4.8 Exercise 20.4: Semi-quantitative Analysis with CCF Analysis
		29.4.9 Exercise 21.1: BDD Building
		29.4.10 Exercise 21.2: Comparison of Probabilistic Results (Disjoint Paths Versus Minimal Cut Sets)
		29.4.11 Exercise 22.1: Unavailability, Failure Frequency and Unreliability Calculations
		29.4.12 Exercise 22.2: Unavailability Calculation with Partial and Full Stroking Tests
		29.4.13 Exercise 22.3: Unavailability Calculation with Common Cause Failures
		29.4.14 Exercise 22.4: Unavailability Calculation with Test Staggering
		29.4.15 Exercise 24.1: Importance Factor Calculations
		29.4.16 Exercise 25.1: Uncertainty Propagation
	Reference
Part IVDynamic Systems and Stochastic  Processes
30 Introduction to Dynamic Systems and Stochastic Processes
	30.1 Miscellaneous Dynamic Aspects
		30.1.1 Dynamic Aspect Linked to System Operation
		30.1.2 Dynamic Aspect Linked to System Maintenance
	30.2 Notion of Stochastic (Random) Processes
	30.3 Dynamic Methods and Tools
	30.4 Systems Typology to Select a Relevant Approach
	References
31 Markovian Modelling
	31.1 Basis of the Classical Markov Approach
		31.1.1 Introduction and Overview of the Markovian Approach
		31.1.2 Graphical Representation of Markov Process
	31.2 Mathematical Foundations
		31.2.1 Basic Formula for Time-Dependent Calculations
		31.2.2 Basic Formula for Asymptotic Calculations
	31.3 Link with Basic Definition
		31.3.1 Preamble
		31.3.2 Availability
		31.3.3 Reliability
		31.3.4 Vesely Failure Rate and Failure Frequency
		31.3.5 Failure Rate and Failure Density
		31.3.6 Comparison λ( t ) Versus λV ( t ) and f( t ) Versus w(t)
		31.3.7 Repair Intensities
		31.3.8 MUT, MDT, MTBF and MTTF
	31.4 Analytical Calculations of Markov Processes
		31.4.1 Classical Calculation Techniques
		31.4.2 Matrix Exponentiation
	31.5 Advanced Modelling
		31.5.1 Failure on Demand and Zero-Duration State
		31.5.2 Sequence Modelling
		31.5.3 Multistate Modelling and Production Availability
		31.5.4 Multiphase Modelling
	31.6 Reducing the Size of the Markov Models
		31.6.1 Aggregation of States
		31.6.2 FT and RBD-Driven Markov Processes
	31.7 Specific Modelling
		31.7.1 CCF Modelling
		31.7.2 Maintenance Modelling
		31.7.3 Cold, Hot and Mixed Redundancy
	31.8 Limitation and Conclusions
	31.9 Associated Exercises
	References
32 Monte Carlo Simulation
	32.1 Introduction to Monte Carlo Simulation
	32.2 History and Principle
	32.3 Generation of Probabilistic Laws
		32.3.1 General Principle for Generating Random Delays
		32.3.2 Random Number Generation
		32.3.3 Simulation of Typical Probabilistic Laws
	32.4 Accuracy of Results
		32.4.1 Accuracy Related to Monte Carlo Itself
		32.4.2 Qualitative Appreciation of the Accuracy
	32.5 Uncertainty Propagation
	32.6 Parameters Changing When Conditions Change
		32.6.1 Introduction and Context
		32.6.2 Updating Occurrence Dates (Principle)
		32.6.3 Various Approaches to Manage the Distribution Changes
		32.6.4 General Approach to Update Failure Dates
		32.6.5 Generalities About the Application to Weibull Distributions
		32.6.6 Detailed Application to Weibull Distributions
		32.6.7 Examples of Application
	32.7 Comparison Between Analytic and Monte Carlo Calculations
	32.8 Associated Exercises
	References
33 Petri Net Modelling
	33.1 Quest for Complex Behaviour Modelling
	33.2 History
	33.3 Petri Net Use Within Automation and Dependability Fields
	33.4 Basic Principles
		33.4.1 Graphical Elements
		33.4.2 Validation of Transitions and Firing Rules
		33.4.3 Managing Conflicts
		33.4.4 Introduction of Delays
		33.4.5 Simple Examples
	33.5 Extensions of the Basic PNs
		33.5.1 Weighted Arcs, Inhibitor Arcs and Repeated Places
		33.5.2 Predicates and Assertions/Messages
		33.5.3 New Validation of Transitions and Firing Rules
	33.6 Other Extensions
		33.6.1 Priority of the Transitions
		33.6.2 Suspended Events (Transition with Memory)
		33.6.3 Probabilistic Switches
		33.6.4 Dynamic Transitions
	33.7 Miscellaneous Modelling Techniques
		33.7.1 Common Cause Failure Modelling
		33.7.2 Modelling Maintenance and Maintenance Supports
	33.8 Undertaking System Modelling
		33.8.1 Modelling of the System
		33.8.2 Monte Carlo Simulation of the Model
		33.8.3 Timetable
		33.8.4 Pre-Processing and Table of Impacted Transitions
		33.8.5 Preventing Endless Loops
		33.8.6 Markov Graph Generation
	33.9 Undertaking System Calculations
		33.9.1 Availability and Unavailability
		33.9.2 MTBF, MUT and MDT
		33.9.3 Reliability and MTTF
		33.9.4 Token Counting Related Results
		33.9.5 Production Availability Calculation
	33.10 Accuracy of Results and Data Uncertainty Handling
	33.11 Building PNs Related to Large Systems
		33.11.1 Main Drawback: Legibility Problem
		33.11.2 Increasing Legibility of Large PNs
		33.11.3 Modularization of Large PNs
		33.11.4 Modelling of Binary Systems
		33.11.5 Modelling of Multistate Systems
	33.12 Coloured Petri Nets
	33.13 Conclusion About PNs
	33.14 Associated Exercises
	References
34 Dynamic Modelling Exercises
	34.1 Markovian Approach Exercises
		34.1.1 Example: Pumping System
		34.1.2 Description of the Exercises Related to the Pumping System
		34.1.3 Solutions of the Exercises Related to the Pumping System
	34.2 Petri Net Approach Exercises
		34.2.1 Example: Service Station
		34.2.2 Description of the Exercises Related to the Service Station
		34.2.3 Solutions of the Exercise Related to the Service Station
	Reference
Part VProduction Availability and Functional Safety (SIL) Modelling and Calculations
35 Production Availability Related Modelling and Calculations
	35.1 Characteristics of Production Systems
		35.1.1 Size and Complexity of the Systems
		35.1.2 Multistate and Multiphase Systems
		35.1.3 Multiple Product Systems
		35.1.4 Multiple Information Sources
	35.2 Classification of Failure and Restoration Events
		35.2.1 Failure Events
		35.2.2 Restoration Events
		35.2.3 Planned Maintenance
	35.3 Characteristics of Production Availability Studies
		35.3.1 Economic Calculations
		35.3.2 Rare Events
	35.4 Case Study for Comparison of Production Availability Models
		35.4.1 Description of the Production System
		35.4.2 Modelling with Flow Diagrams
		35.4.3 Modelling with Reliability Block Diagrams
		35.4.4 Modelling with Markov Graphs
		35.4.5 Modelling with Petri Nets
	References
36 Functional Safety Related Modelling and Calculations
	36.1 Introduction and Standardization
	36.2 Safety Integrity Concepts
		36.2.1 Establishing the Safety Integrity Levels (SIL) Requirements
		36.2.2 Low Demand Versus High Demand Mode of Operation
		36.2.3 Probabilistic Requirements: PFDavg and PFH
		36.2.4 Failure Classification
		36.2.5 Loss-of-Power Versus Emission-of-Power Safety Systems
		36.2.6 Safe Failure Fraction: The False Good Idea
		36.2.7 Fault Tolerance (Architectural Constraints)
		36.2.8 Use of k Out of n Logic
	36.3 Probabilistic Calculations
		36.3.1 Input Data Needs and Conservativeness
		36.3.2 Simplified Analytical Approach
		36.3.3 Markovian Approach
		36.3.4 Boolean Approach
		36.3.5 Petri Net Approach
		36.3.6 Uncertainty Handling in SIL Calculations
	36.4 Conclusions
	36.5 Associated Exercises
	References
Part VIStandardization, Data Collection and Uncertainties
37 Standardization
	37.1 Introduction to Standardization
	37.2 Standardization Versus Regulation and Certification
	37.3 Standardization Organization Overview
		37.3.1 Standardization Bodies
		37.3.2 Development of a Standard
		37.3.3 Type and Content of Standards
	37.4 Safety and Dependability Related Standardization
	37.5 Concluding Remarks About Standardization
	References
38 Data Collection and Uncertainties
	38.1 Introduction
	38.2 The Bare Necessity of Input Data
	38.3 Data Collection Standards and Databases
		38.3.1 IEC and ISO Data Collection Related Standards
		38.3.2 Databases
	38.4 Reliability Data Estimation
	38.5 Data Uncertainty Modelling
		38.5.1 Data Accuracy Versus Field Feedback
		38.5.2 Uniform and Triangular Distributions: Expert Judgment
		38.5.3 Chi-Square Distribution: Statistics from Field Feedback
		38.5.4 Bayesian Approach and Gamma Distribution
		38.5.5 Log-Normal Distribution: Practical Approach
	References
Index