Chapter 1. Basic Concepts 1

1.1. Introduction 1

1.2. Definition of terms 1

1.2.1. Risk 1

1.2.2. Time definitions 2

1.2.3. Failures and repairs 4

1.2.4. IEC 61508 terms 8

1.3. Definition of parameters 10

1.3.1. Reliability 10

1.3.2. Maintainability 12

1.3.3. Availability and production availability 12

1.3.4. Dependability 13

1.3.5. Definitions used by maintenance engineers 13

1.3.6. Definitions used in the refinery industry 14

1.4. The exponential law/the constant failure rate 14

1.4.1. Reliability 14

1.4.2. Validity 15

1.4.3. Oil and gas industry 16

1.5. The bathtub curve 16

1.5.1. Meaning 16

1.5.2. Useful life and mission life 18

1.5.3. Validity 18

1.5.4. Oil and gas industry 18

Chapter 2. Mathematics for Reliability 21

2.1. Introduction 21

2.2. Basis of probability and statistics 22

2.2.1. Boolean algebra 22

2.2.2. Probability relations 22

2.2.3. Probability distributions 24

2.2.4. Characteristics of probability distributions 24

2.2.5. Families and conjugates 26

2.3. Formulae and theorems 27

2.3.1. Combinatorial analysis 27

2.3.2. Central limit theorem 28

2.3.3. Chebyshev’s inequality 28

2.3.4. Laws of large numbers 28

2.3.5. Supporting functions and distributions 29

2.3.6. Bayes’ theorem 30

2.4. Useful discrete probability distributions 32

2.4.1. Binomial distribution 33

2.4.2. Poisson distribution. 33

2.5. Useful continuous probability distributions 35

2.5.1. Exponential distribution 35

2.5.2. Uniform distribution 36

2.5.3. Triangular distribution 37

2.5.4. Normal distribution 38

2.5.5. Log-normal distribution 40

2.5.6. Weibull distribution 43

2.5.7. Gamma distribution 44

2.5.8. Beta distribution 45

2.5.9. Chi-squared distribution 46

2.5.10. Fisher-Snedecor distribution 46

2.6. Statistical estimates 47

2.6.1. Estimates 47

2.6.2. Calculation of point estimate 47

2.6.3. Calculation of confidence interval 50

2.6.4. Heterogeneous samples 52

2.6.5. Implementation 53

2.7. Fitting of failure distribution 53

2.7.1. Principle 53

2.7.2. Median rank method 54

2.7.3. Implementation 55

2.8. Hypothesis testing 57

2.8.1. Principle 57

2.8.2. Existing tests. 58

2.8.3. Implementation 58

2.9. Bayesian reliability 60

2.9.1. Definition 60

2.9.2. Use of Bayes’ theorem 61

2.9.3. Bayesian inference 61

2.9.4. Selection of the prior probability distribution 62

2.9.5. Determination of the posterior probability distribution 62

2.9.6. Bayesian credibility interval 64

2.10. Extreme value probability distributions 65

2.10.1. Meaning. 65

2.10.2. The three extreme value probability distributions 65

2.10.3. Use in the industry 66

Chapter 3. Assessment of Standard Systems 67

3.1. Introduction 67

3.2. Single item 67

3.2.1. Availability 68

3.2.2. Number of failures 69

3.3. System reliability 70

3.3.1. Series systems 70

3.3.2. Parallel systems 72

3.4. Specific architectures 73

3.4.1. Method of analysis 73

3.4.2. Redundant item system 74

3.5. On-guard items 76

3.5.1. Unrevealed failures 76

3.5.2. Full formula 77

3.5.3. Optimum proof test duration 79

Chapter 4. Classic Methods 81

4.1. Introduction 81

4.2. Failure Mode and Effects Analysis 81

4.2.1. Conventional Failure Mode and Effects Analysis/Failure Mode,Effects and Criticality Analysis 81

4.2.2. Functional/hardware FMEA 84

4.2.3. Case study 84

4.3. Fault trees 89

4.3.1. Conventional fault trees 89

4.3.2. Fault tree extensions 93

4.3.3. Facilities provided by software packages 94

4.3.4. Case study 94

4.4. Reliability block diagrams 98

4.4.1. Conventional RBDs 98

4.4.2. RBD extension 102

4.4.3. Facilities provided by software packages 103

4.4.4. Case study 103

4.5. Monte Carlo method 104

4.5.1. Principle 104

4.5.2. Use for production availability and reliability 106

4.5.3. How many runs are enough? 107

Chapter 5. Petri Net Method 109

5.1. Introduction 109

5.2. Petri nets 110

5.2.1. Definition 110

5.2.2. Mathematical properties 111

5.2.3. Petri net construction 112

5.2.4. GRAFCET 117

5.3. IEC 62551 extensions 117

5.3.1. Extensions to structure 117

5.3.2. Modified execution rules 120

5.4. Additional extensions 121

5.4.1. Extensions to structure 121

5.4.2. Modified execution rules 122

5.5. Facilities provided by software packages 123

5.5.1. Additional extensions to structure 123

5.5.2. Modified execution rules 123

5.5.3. Petri net processing 123

5.5.4. Results 123

5.6. Petri net construction 124

5.6.1. Petri net modeling 124

5.6.2. Minimizing the risk of error input 124

5.6.3. Petri net checking 124

5.6.4. Petri net validation 125

5.7. Case study 125

5.7.1. System description 125

5.7.2. Petri net model 126

Chapter 6. Sources of Reliability Data 133

6.1. Introduction 133

6.2. The OREDA project 133

6.2.1. History 133

6.2.2. Project management and organization 135

6.2.3. Description of OREDA 2015 handbooks 135

6.2.4. Use of the data tables 137

6.2.5. Use of the additional tables 141

6.2.6. Reliability database and data analysis software 143

6.2.7. Data collection software 144

6.3. The PDS handbook 144

6.3.1. History 144

6.3.2. Description of the handbook 145

6.3.3. Use of the handbook 145

6.4. Reliability Analysis Center/Reliability Information Analysis Center publications 145

6.4.1. History 145

6.4.2. Non-electronic Part Reliability Data handbook 146

6.4.3. FMD 146

6.4.4. NONOP 146

6.4.5. Use of the publications 146

6.5. Other publications 147

6.5.1. EXIDA handbooks 147

6.5.2. Electrical items 147

6.5.3. Pipelines 148

6.5.4. Flexibles 149

6.5.5. Miscellaneous 149

6.6. Missing information 150

Chapter 7. Use of Reliability Test and Field Data 151

7.1. Introduction 151

7.2. Reliability test data 151

7.2.1. Principle 151

7.2.2. Test organization 152

7.2.3. Assessment of failure rate 152

7.3. Field data 154

7.3.1. Principle 154

7.3.2. Data collection organization 155

7.3.3. Assessment of failure rate 155

7.3.4. Assessment of probability to fail upon demand 156

7.3.5. Assessment of MRT 156

7.3.6. Case study 156

7.4. Accelerated tests 157

7.4.1. Principle 157

7.4.2. Example 158

7.4.3. Highly accelerated tests 159

7.5. Reliability growth 159

7.5.1. Principle 159

7.5.2. Main models 159

Chapter 8. Use of Expert Judgment. 163

8.1. Introduction 163

8.2. Basis 164

8.2.1. Definitions 164

8.2.2. Protocol for expert elicitation 164

8.2.3. Role of the facilitator 165

8.3. Characteristics of the experts 166

8.3.1. Definition 166

8.3.2. Selection 166

8.3.3. Biases 167

8.3.4. Expert weighting 168

8.3.5. Expert dependence 169

8.3.6. Aggregation of judgments 169

8.4. Use of questionnaires 169

8.4.1. Conditions of use 169

8.4.2. The Delphi method 170

8.4.3. Case study 171

8.5. Use of interactive group 173

8.5.1. Number of experts 173

8.5.2. Procedure. 173

8.6. Use of individual interviews 174

8.6.1. Conditions of use 174

8.6.2. Case study 174

8.7. Bayesian aggregation of judgment 175

8.7.1. Form of information provided by experts 175

8.7.2. Assessment of failure rate (or MTBF) 176

8.7.3. Assessment of probability of failure upon demand 177

8.8. Validity of expert judgment 177

Chapter 9. Supporting Topics 179

9.1. Introduction 179

9.2. Common cause failures 179

9.2.1. Introduction 179

9.2.2. Definition 180

9.2.3. Defenses against CCF 181

9.2.4. CCF modeling with the beta-factor method 182

9.2.5. CCF modeling with the shock method 185

9.2.6. Extension of the beta-factor model: the PDS method 188

9.2.7. Field data 189

9.2.8. Impact of CCF on system reliability 190

9.2.9. Impact of testing policy on CCF 191

9.2.10. Impact of CCF on system production availability 194

9.2.11. Benchmark on CCF assessment 194

9.3. Mechanical reliability 195

9.3.1. Characteristics 195

9.3.2. Stress-strength interference 195

9.3.3. Empirical reliability relationships 197

9.3.4. Comparison with system (constant failure rate) approach 199

9.4. Reliability of electronic items 199

9.4.1. Characteristics 199

9.4.2. MIL-HDBK-217 200

9.4.3. UTE-C-80811 201

9.4.4. Other reliability data books 201

9.4.5. EPRD 203

9.4.6. Effect of dormancy period 203

9.4.7. Common cause failures 203

9.4.8. Comparison of previsions 204

9.4.9. Use in the oil and gas industry 205

9.5. Human reliability 205

9.5.1. Human factors 205

9.5.2. Human reliability in the nuclear industry 205

9.5.3. Evaluation of HRA techniques 206

9.5.4. Human reliability in the oil and gas industry 206

Chapter 10. System Reliability Assessment 209

10.1. Introduction 209

10.2. Definition of reliability target 209

10.2.1. Absolute reliability target 209

10.2.2. Risk target 210

10.3. Methodology of system reliability study 211

10.3.1. Overall description 211

10.3.2. Step 1: system analysis 212

10.3.3. Step 2: qualitative analysis. 212

10.3.4. Step 3: quantitative data selection 212

10.3.5. Step 4: system reliability modeling 214

10.3.6. Step 5: synthesis 214

10.4. SIL studies 214

10.4.1. Introduction 214

10.4.2. SIL assignment 214

10.4.3. SIL demonstration 217

10.5. Description of the case study 217

10.5.1. Origin of the risk 217

10.5.2. Description of the standard SIF 219

10.5.3. Risk assessment 219

10.6. System analysis 220

10.6.1. Description of HIPS functioning 220

10.7. Qualitative analysis 221

10.7.1. FMEA 221

10.7.2. CCF analysis 223

10.8. Quantitative data selection 225

10.8.1. Selection of reliability data 225

10.8.2. Collection of proof test data 225

10.8.3. CCF quantification 226

10.9. System reliability modeling 226

10.9.1. Building of system reliability model 226

10.9.2. System reliability calculation 226

10.10. Synthesis 232

10.10.1. Conclusions 232

10.10.2. Recommendations 233

10.11. Validity of system reliability assessments 234

10.11.1. Reports 234

10.11.2. Conclusions 234

Chapter 11. Production Availability Assessment 235

11.1. Introduction 235

11.2. Definition of production availability target 235

11.2.1. Absolute production availability target 235

11.2.2. Economic target 235

11.3. Methodology 236

11.3.1. Events considered in production availability assessments 236

11.3.2. Overall description 236

11.3.3. Step 1: system analysis 238

11.3.4. Step 2: quantitative data selection 238

11.3.5. Step 3: production availability assessment 238

11.3.6. Step 4: synthesis 238

11.4. System analysis 239

11.4.1. Determination of system running modes 239

11.4.2. Item failure analysis 242

11.5. Quantitative data selection 244

11.5.1. Selection of reliability data 244

11.5.2. Collection of operational data 245

11.6. Production availability assessment 246

11.6.1. Building of production availability model 246

11.6.2. Production availability calculations 246

11.7. Synthesis 248

11.7.1. Main results 248

11.7.2. Additional economic parameters 249

11.7.3. Flared gas 251

11.7.4. Other results 253

11.7.5. Recommendations 256

11.8. Uncertainty on the reliability parameters 256

11.9. Validity of production availability assessments 257

Chapter 12. Management of Production

Availability and Reliability 259

12.1. Introduction 259

12.2. Principles of dependability management 260

12.2.1. Dependability property management 260

12.2.2. Phasing of the management 260

12.2.3. Lifecycle costing and dependability 261

12.3. Technical specifications 262

12.3.1. Contents. 262

12.3.2. Reliability specification 262

12.3.3. Production availability specification 263

12.4. Reliability and production availability program 264

12.4.1. Contents. 264

12.4.2. Reliability program 266

12.4.3. Production availability program 267

12.5. Validation of system reliability 267

12.5.1. Reliability data collection 267

12.5.2. Random failures 268

12.5.3. Common cause failures 268

12.6. Validation of production availability 268

12.6.1. Useful life 268

12.6.2. Reliability data 269

12.6.3. Production data 269

12.6.4. Use of production availability model 269

Appendices 271

Appendix 1. Notations and Abbreviations 273

Appendix 2. Markov Chain 283

Appendix 3. Comparison of Modeling Methods 293

Appendix 4. Solutions of Exercises. 301

Bibliography 315

Index 323