Table of Contents
Preface viii
Symbols x
1 Terminologies in process safety engineering 1
1.1 Plant systems 1
1.2 Safety systems 2
2 Derivation of basic formulae 8
2.1 Introduction 8
2.2 Failure prediction 8
2.3 Reliability function 8
2.4 Hazard function 9
2.5 Failure probability density function 9
2.6 The exponential reliability function R(t) 10
2.7 The exponential density function f(t) 12
2.8 The exponential cumulative function F(t) 13
2.9 Summary and final comments 14
3 Unavailability, safety and changes of state 15
3.1 Failure modes and plant unavailability 15
3.2 Failure rate components 15
3.3 Changes of state 17
4 Proof testing 27
4.1 Introduction 27
4.2 Proof-testing philosophies 27
4.3 Proof-testing procedures 28
4.4 System proof testing 30
4.5 Proof testing of the single safety channel 33
5 Data and mean fractional dead times 34
5.1 Data for failure probability evaluations 34
5.2 Systems mean fractional dead times 38
6 Logical network principles 44
6.1 Introduction 44
6.2 Binary variables 44
6.3 Logic gates - symbolic notations 46
6.4 Truth tables 47
6.5 Combinations through logic gates 48
6.6 Dimensional criteria 52
7 Fault trees 54
7.1 Introduction 54
7.2 Fault-tree software programs 54
7.3 Logic philosophy - success or failure 55
7.4 Fault trees and event trees 56
7.5 Fault-tree rationalization 57
7.6 Cut sets 57
7.7 Categories of cut sets 60
7.8 General principles of fault-tree construction 61
7.9 Boolean reduction 65
7.10 Process system - demonstration fault-tree study 65
8 Mathematical modelling 73
8.1 Introduction 73
8.2 Basis of the mathematical model 74
8.3 Evaluation of the mathematical model 75
8.4 Quantities in risk assessment modelling 75
8.5 Logic gates in systems safety modelling 78
8.6 Boolean combinations at logic gates 79
8.7 Probabilistic - definition 82
8.8 Probability expression nomenclatures 83
8.9 Definitions of probability - partly reversible state 83
8.10 Definitions of probability - reversible state 83
8.11 Higher-order probability terms in gate outputs 84
8.12 Combining higher-order probabilities 84
8.13 Rate combinations at the logical OR gate 85
8.14 Probability combinations at the logical OR gate 86
8.15 Rate combinations at the logical AND gate 91
8.16 Probability combinations at the logical AND gate 94
8.17 Rate and probability inputs at the logical AND gate 96
8.18 Rate combinations at majority voting gates 98
8.19 Probability combinations at majority voting gates 99
8.20 High and low demand rates in risk assessment 101
9 Mathematical modelling of human failures 107
9.1 Introduction 107
9.2 The human element 108
9.3 Interpretation of data 109
9.4 Aspects of human failure 110
9.5 Human and human-equipment failure combinations at logic gates 110
9.6 Combinations at the logical OR gate 112
9.7 Combinations at the logical AND gate 114
9.8 Combinations in majority voting logic 118
10 Modelling common-mode failures 120
10.1 Introduction 120
10.2 Definition of terms 120
10.3 Symbols 121
10.4 The nature of common-mode failure in assessment 122
10.5 The logical approach to common-mode failure assessment 126
10.6 Common-mode analysis from independent minimal cut sets 127
10.7 Common-mode assessment methodology 132
10.8 Elementary system study 137
Appendices - tutorial projects
A Qualitative assessment of safety system reliability 147
B Quantitative assessment of safety system reliability 152
C Reliability case study of an automatic protective system 162
D Reliability case study of an automatic fire valve based on failure mode and effect analysis 184
Index 193
