# Foundations of Risk Analysis, 2nd Edition

# Foundations of Risk Analysis, 2nd Edition

ISBN: 978-1-119-96697-5

Apr 2012

228 pages

## Description

*Foundations of Risk Analysis* presents the issues core to risk analysis – understanding what risk means, expressing risk, building risk models, addressing uncertainty, and applying probability models to real problems. The author provides the readers with the knowledge and basic thinking they require to successfully manage risk and uncertainty to support decision makin*g.* This updated edition reflects recent developments on risk and uncertainty concepts, representations and treatment.

New material in *Foundations of Risk Analysis* includes:

- An up to date presentation of how to understand, define and describe risk based on research carried out in recent years.
- A new definition of the concept of vulnerability consistent with the understanding of risk.
- Reflections on the need for seeing beyond probabilities to measure/describe uncertainties.
- A presentation and discussion of a method for assessing the importance of assumptions (uncertainty factors) in the background knowledge that the subjective probabilities are based on
- A brief introduction to approaches that produce interval (imprecise) probabilities instead of exact probabilities.

In addition the new version provides a number of other improvements, for example, concerning the use of cost-benefit analyses and the As Low As Reasonably Practicable (ALARP) principle.

*Foundations of Risk Analysis* provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty.

**Preface to the second edition ix**

**Preface to the first edition xi**

**1 Introduction 1**

1.1 The importance of risk and uncertainty assessments 1

1.2 The need to develop a proper risk analysis framework 4

Bibliographic notes 6

**2 Common thinking about risk and risk analysis 7**

2.1 Accident risk 7

2.1.1 Accident statistics 7

2.1.2 Risk analysis 11

2.1.3 Reliability analysis 24

2.2 Economic risk 28

2.2.1 General definitions of economic risk in business and project management 28

2.2.2 A cost risk analysis 30

2.2.3 Finance and portfolio theory 31

2.2.4 Treatment of risk in project discounted cash flow analysis 34

2.3 Discussion and conclusions 36

2.3.1 The classical approach 36

2.3.2 The Bayesian paradigm 37

2.3.3 Economic risk and rational decision-making 39

2.3.4 Other perspectives and applications 40

2.3.5 Conclusions 43

Bibliographic notes 43

**3 How to think about risk and risk analysis 47**

3.1 Basic ideas and principles 47

3.1.1 Background knowledge 52

3.1.2 Models and simplifications in probability considerations 53

3.1.3 Observable quantities 53

3.2 Economic risk 54

3.2.1 A simple cost risk example 54

3.2.2 Production risk 57

3.2.3 Business and project management 59

3.2.4 Investing money in a stock market 60

3.2.5 Discounted cash flow analysis 61

3.3 Accident risk 62

3.4 Discussion 63

Bibliographic notes 68

**4 How to assess uncertainties and specify probabilities 71**

4.1 What is a good probability assignment? 72

4.1.1 Criteria for evaluating probabilities 72

4.1.2 Heuristics and biases 74

4.1.3 Evaluation of the assessors 75

4.1.4 Standardization and consensus 76

4.2 Modeling 76

4.2.1 Examples of models 77

4.2.2 Discussion 78

4.3 Assessing uncertainty of *Y* 79

4.3.1 Assignments based on classical statistical methods 80

4.3.2 Analyst judgments using all sources of information 81

4.3.3 Formal expert elicitation 82

4.3.4 Bayesian analysis 83

4.4 Uncertainty assessments of a vector **X** 91

4.4.1 Cost risk 91

4.4.2 Production risk 93

4.4.3 Reliability analysis 94

4.5 Discussion 97

4.5.1 Risk analysis and science 97

4.5.2 Probability and utility 98

4.5.3 Probability and knowledge 99

4.5.4 Probability models 99

4.5.5 Firm and vague probabilities 100

4.5.6 The need for seeing beyond probabilities 100

4.5.7 Interval (imprecise) probabilities 101

4.5.8 Example of interval (imprecise) probabilities in a risk analysis setting 102

4.5.9 Possibility theory 103

4.5.10 Example of interval (imprecise) probabilities in a risk analysis context using possibility theory 104

4.5.11 Final comments 106

Bibliographic notes 108

**5 How to use risk analysis to support decision-making 111**

5.1 What is a good decision? 112

5.1.1 Features of a decision-making model 113

5.1.2 Decision-support tools 114

5.1.3 Discussion 119

5.2 Some examples 122

5.2.1 Accident risk 122

5.2.2 Scrap in place or complete removal of plant 125

5.2.3 Production system 130

5.2.4 Reliability target 131

5.2.5 Health risk 133

5.2.6 Warranties 135

5.2.7 Offshore development project 136

5.2.8 Risk assessment: National sector 138

5.2.9 Multi-attribute utility example 140

5.3 Risk problem classification schemes 143

5.3.1 A scheme based on consequences and uncertainties 143

5.3.2 A scheme based on closeness to hazard and level of authority 147

Bibliographic notes 158

**6 Summary and conclusions 161**

**Appendix A: Basic theory of probability and statistics 165**

A.1 Probability theory 165

A.1.1 Types of probabilities 165

A.1.2 Probability rules 168

A.1.3 Random quantities (random variables) 172

A.1.4 Some common discrete probability distributions (models) 176

A.1.5 Some common continuous distributions (models) 178

A.1.6 Some remarks on probability models and their parameters 182

A.1.7 Random processes 183

A.2 Classical statistical inference 184

A.2.1 Nonparametric estimation 184

A.2.2 Estimation of distribution parameters 185

A.2.3 Testing hypotheses 187

A.2.4 Regression 188

A.3 Bayesian inference 189

A.3.1 Statistical (Bayesian) decision analysis 191

Bibliographic notes 192

**Appendix B: Terminology 193**

B.1 Risk management: Relationships between key terms 195

**References 197**

**Index 207**

""The book provides a framework for understanding, conducting and using risk analysis suitable for advanced undergraduates, graduates, analysts and researchers from statistics, engineering, finance, medicine and the physical sciences, as well as for managers facing decision making problems involving risk and uncertainty."" (*Zentralblatt MATH*, 1 December 2012)