First published 2018 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.

Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:

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The rights of Alain Leroy to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.

Library of Congress Control Number: 2018930621

British Library Cataloguing-in-Publication Data

A CIP record for this book is available from the British Library

ISBN 978-1-78630-168-0

Table of Contents

Cover

Preface

1 Basic Concepts

1.1. Introduction
1.2. Definition of terms
1.3. Definition of parameters
1.4. The exponential law/the constant failure rate
1.5. The bathtub curve

2 Mathematics for Reliability

2.1. Introduction
2.2. Basis of probability and statistics
2.3. Formulae and theorems
2.4. Useful discrete probability distributions
2.5. Useful continuous probability distributions
2.6. Statistical estimates
2.7. Fitting of failure distribution
2.8. Hypothesis testing
2.9. Bayesian reliability
2.10. Extreme value probability distributions

3 Assessment of Standard Systems

3.1. Introduction
3.2. Single item
3.3. System reliability
3.4. Specific architectures
3.5. On-guard items

4 Classic Methods

4.1. Introduction
4.2. Failure Mode and Effects Analysis
4.3. Fault trees
4.4. Reliability block diagrams
4.5. Monte Carlo method

5 Petri Net Method

5.1. Introduction
5.2. Petri nets
5.3. IEC 62551 extensions
5.4. Additional extensions
5.5. Facilities provided by software packages
5.6. Petri net construction
5.7. Case study

6 Sources of Reliability Data

6.1. Introduction
6.2. The OREDA project
6.3. The PDS handbook
6.4. Reliability Analysis Center/Reliability Information Analysis Center publications
6.5. Other publications
6.6. Missing information

7 Use of Reliability Test and Field Data

7.1. Introduction
7.2. Reliability test data
7.3. Field data
7.4. Accelerated tests
7.5. Reliability growth

8 Use of Expert Judgment

8.1. Introduction
8.2. Basis
8.3. Characteristics of the experts
8.4. Use of questionnaires
8.5. Use of interactive group
8.6. Use of individual interviews
8.7. Bayesian aggregation of judgment
8.8. Validity of expert judgment

9 Supporting Topics

9.1. Introduction
9.2. Common cause failures
9.3. Mechanical reliability
9.4. Reliability of electronic items
9.5. Human reliability

10 System Reliability Assessment

10.1. Introduction
10.2. Definition of reliability target
10.3. Methodology of system reliability study
10.4. SIL studies
10.5. Description of the case study
10.6. System analysis
10.7. Qualitative analysis
10.8. Quantitative data selection
10.9. System reliability modeling
10.10. Synthesis
10.11. Validity of system reliability assessments

11 Production Availability Assessment

11.1. Introduction
11.2. Definition of production availability target
11.3. Methodology
11.4. System analysis
11.5. Quantitative data selection
11.6. Production availability assessment
11.7. Synthesis
11.8. Uncertainty on the reliability parameters
11.9. Validity of production availability assessments

12 Management of Production Availability and Reliability

12.1. Introduction
12.2. Principles of dependability management
12.3. Technical specifications
12.4. Reliability and production availability program
12.5. Validation of system reliability
12.6. Validation of production availability

Appendices

Appendix 1: Notations and Abbreviations
Appendix 2: Markov Chain
Appendix 3: Comparison of Modeling Methods
Appendix 4: Solutions of Exercises

Bibliography

Index

End User License Agreement

List of Tables

1 Basic Concepts

Table 1.1. The four safety integrity levels

2 Mathematics for Reliability

Table 2.1. Useful rules of Boolean algebra
Table 2.2. Median rank calculation for example 2.6
Table 2.3. Validity of Benard’s formula
Table 2.4. Calculations of Kolmogorov test statistic for example 2.7
Table 2.5. Characteristics of the product of two specific conjugates

3 Assessment of Standard Systems

Table 3.1. Reliability data for items in Figure 3.4
Table 3.2. Value of PFD_avg for five redundancy configurations (without CCF)

4 Classic Methods

Table 4.1. Reliability and test data for case study 4.3.4

6 Sources of Reliability Data

Table 6.1. Values of estimates assuming homogeneous and heterogeneous samples

8 Use of Expert Judgment

Table 8.1. Comparison of the three elicitation methods
Table 8.2. Comparison estimate of expert-true value
Table 8.3. Formula for assessing constant failure rate and probability to fail upon demand

9 Supporting Topics

Table 9.1. Weight of the factors in IEC 61508 table for assessing β
Table 9.2. Parameters of the shock method versus beta-factors
Table 9.3. PDS method: value of main C_MooN
Table 9.4. Impact of the CCF on system reliability
Table 9.5. MIL-HDBK-217 environmental factors and oil and gas units
Table 9.6. Comparison of reliability predictions according to [IMD 09]
Table 9.7. Comparison of reliability predictions according to [EPS 05]

10 System Reliability Assessment

Table 10.1. Examples of SIF
Table 10.2. RRF and SIL equivalence
Table 10.3. Selected reliability and proof test data

11 Production Availability Assessment

Table 11.1. Mean production availability vs. number of runs (Monte Carlo simulation)
Table 11.2. Example of additional results: use of support vessels for subsea plants
Table 11.3. Comparison of results considering the uncertainty on the reliability parameters

Appendix 2: Markov Chain

Table A2.1. Useful Laplace transforms

Appendix 3: Comparison of Modeling Methods

Table A3.1. Reliability and capacity data
Table A3.2. Results

List of Illustrations

1 Basic Concepts

Figure 1.1. Risk in the two-dimension space
Figure 1.2. Failure-to-repair cycle
Figure 1.3. Relationship of failure causes, failure modes and failure effects
Figure 1.4. The three phases of use of an item
Figure 1.5. The exponential law
Figure 1.6. The bathtub curve
Figure 1.7. Effect of preventive maintenance on the failure rate

2 Mathematics for Reliability

Figure 2.1. Graph of the pmf of the binomial distribution (n = 5, p = 0.3)
Figure 2.2. Graph of the pmf of the Poisson distribution (m = 0.1)
Figure 2.3. Graph of the pdf of the negative exponential distribution
Figure 2.4. Graph of M(t) with μ =10^–1 hr^–1
Figure 2.5. Graph of the pdf of the uniform distribution (a = 2 hr, b = 10 hr)
Figure 2.6. Graph of the pdf of the triangular distribution (a = 2 hr, c = 5 hr, b = 10 hr)
Figure 2.7. Graph of the pdf of the normal distribution ( μ = 5 hr, σ = 2 hr)
Figure 2.8. Graph of the pdf of the log-normal distribution ( μ = 5 hr, σ = 3 hr )
Figure 2.9. Graph of the pdf of a Weibull distribution (β = 0.5 hr, η =2 hr, γ = 0)
Figure 2.10. Fitting of data of example 2.6

3 Assessment of Standard Systems

Figure 3.1. Markov graph for assessing the availability of a repairable item
Figure 3.2. Availability of a repairable item
Figure 3.3. A series system of n items
Figure 3.4. Water booster injection pumping system
Figure 3.5. A parallel system (n items)
Figure 3.6. Markov graph for 1oo2 non-repairable active system
Figure 3.7. Markov graph for 1oo2 repairable active system

4 Classic Methods

Figure 4.1. Example of criticality matrix
Figure 4.2. Case study: functional analysis table
Figure 4.3. Case study: FMECA worksheet
Figure 4.4. FTA: OR gate
Figure 4.5. FTA: AND gate
Figure 4.6. FTA: 2003 gate
Figure 4.7. FTA: basic event
Figure 4.8. FTA: undeveloped event
Figure 4.9. FTA: transfer symbol
Figure 4.10. Fault tree for case study 4.3.4
Figure 4.11. PFD(t) curve for case study 4.3.4
Figure 4.12. RBD: basic block
Figure 4.13. Series RBD
Figure 4.14. Parallel RBD, two items on active redundancy
Figure 4.15. Parallel RBD, one item on standby redundancy
Figure 4.16. RBD with repeated event
Figure 4.17. RBD with repeated event: B failed
Figure 4.18. RBD with repeated event: B running
Figure 4.19. Example of dynamic RBD
Figure 4.20. RBD for case study section 4.4.4

5 Petri Net Method

Figure 5.1. Items of a Petri net
Figure 5.2. Petri net before and after firing
Figure 5.3. Petri nets for exercise 5.1
Figure 5.4. Petri nets for exercise 5.2
Figure 5.5. Petri net for the failure-to-repair cycle of HE1
Figure 5.6. Petri net for the repair team synchronized with the failure-to-repair cycle of HE1
Figure 5.7. Petri net for the production availability levels.
Figure 5.8. Petri net for example 5.2
Figure 5.9. Example of weighted and inhibitor² arcs
Figure 5.10. Petri net for example 5.3
Figure 5.11. Petri net for example 5.4
Figure 5.12. RBD of exercise 5.3
Figure 5.13. Example of reset arc
Figure 5.14. Modeling of the probability of failure upon demand
Figure 5.15. Petri net for the HP compressor of train A
Figure 5.16. Petri net for the number of HP trains running
Figure 5.17. Petri net for the capital spare part of the HP compressor
Figure 5.18. Petri net for the calendar

6 Sources of Reliability Data

Figure 6.1. Reliability data table (first page only) for pumps
Figure 6.2. Maintainable item versus failure mode (second page only) for pumps
Figure 6.3. Failure mechanism versus failure mode (second page only) for pumps

9 Supporting Topics

Figure 9.1. Fault tree without CCF
Figure 9.2. Fault tree with CCF
Figure 9.3. PFD(t) without CCF (test interval = 6 months)
Figure 9.4. PFD(t) with CCF (test interval = 6 months)
Figure 9.5. PFD(t) without CCF and staggered testing (test interval = 6 months)
Figure 9.6. PFD(t) with CCF and staggered testing

10 System Reliability Assessment

Figure 10.1. Typical risk acceptability matrix
Figure 10.2. Steps in the system reliability assessment methodology
Figure 10.3. Instrumentation and valves on first-stage separator liquid outlet
Figure 10.4. Standard SIF
Figure 10.5. High integrity protection system
Figure 10.6. FMEA worksheet
Figure 10.7. Fault tree for unwanted event “Standard SIF failure to act”
Figure 10.8. Fault tree for unwanted event “HIPS failure to act"
Figure 10.9. Graph of PFD(t) for HIPS⁹
Figure 10.10. Distribution of PFD(t) within SIL for HIPS
Figure 10.11. Fault tree for unwanted event “HIPS and standard SIF failure to act”
Figure 10.12. Graph of PFD(t) for HIPS + standard SIF
Figure 10.13. Distribution of PFD(t) within SIL for HIPS +standard SIF
Figure 10.14. Preventive barrier for exercise 10.1

11 Production Availability Assessment

Figure 11.1. Steps in the plant production availability assessment methodology
Figure 11.2. Functional breakdown and item failure analysis
Figure 11.3. Functional diagram for 2x100% items
Figure 11.4. Functional diagram for separation function with off-line item
Figure 11.5. Functional diagram for oil export function with buffer tanks
Figure 11.6. Functional diagram for a section of a dehydration unit
Figure 11.7. Example of FMEA worksheet
Figure 11.8. Annual oil production availability over 20 years for 100 runs (Monte Carlo simulation)
Figure 11.9. Annual oil production availability over 20 years for 1,000 runs (Monte Carlo simulation)
Figure 11.10. Annual available oil export
Figure 11.11. Oil production availability distribution (given by the Monte Carlo simulation)
Figure 11.12. Annual oil production availability (over 12 years)
Figure 11.13. Mean flared gas volume in Mscm and by year

Appendix 2: Markov Chain

Figure A2.1. Markov graph for two-item system
Figure A2.2. Markov graph for example A2.1
Figure A2.3. Multi-phase Markov graph

Appendix 3: Comparison of Modeling Methods

Figure A3.1. RBD of the test case
Figure A3.2. Markov graph assuming no failure of item E_i
Figure A3.3. Histogram of the 100 samples
Figure A3.4. Petri net for item C₂
Figure A3.5. Petri net for repair teams of items C_iD_i

Appendix 4: Solutions of Exercises

Figure A4.1. Graph for exercise 2.3
Figure A4.2. Fault tree for exercise 4.1
Figure A4.3. Exercise 5.2: Petri net after firing of t2
Figure A4.4. Exercise 5.2: Petri net after firing of t3
Figure A4.5. Exercise 5.2: Petri net after firing of t1
Figure A4.6. Exercise 5.3. Petri net for production levels
Figure A4.7. Exercise 5.3: Petri net for item B
Figure A4.8. Exercise 5.3: Petri net for item A
Figure A4.9. Exercise 5.3: Petri net for item C
Figure A4.10. Fault tree for exercise 10.1 without CCF
Figure A4.11. Fault tree for exercise 10.1 with CCF
Figure A4.12. Markov graph for exercise A2.1
Figure A4.13. Markov graph for exercise A2.2

Preface

Any industry is continuously modifying its processes, its organization and its management to cater for new problems. These modifications are part of the day-to-day job as long as these new problems look like the steps of a staircase. This approach is no longer valid if these new problems look like a wall: new equipment, new techniques, new principles, etc., are to be implemented. Reliability engineering emerged as an answer to some of these problems along the years; it finds its roots as a new discipline on the fact that “at the beginning of the Korean War about 70% of Navy electronic gear did not operate properly” [KEC 02]. Reliability engineering soon became part of the equipment development programs in the defense industry and in the civil nuclear industry, with an emphasis on safety performances.

Although it can be considered that the oil and gas industry started to implement these techniques by the mid-70’s with the beginning of subsea production, it took around one more decade for the industry to use them on a regular basis. However, the oil and gas industry is the first industry to perform production availability studies on a regular basis and as part of its plant development programs (offshore units first).

The aim of this book is to provide all of the information requested for efficient specification, assessment, follow-up and management of production availability and reliability characteristics of petroleum systems (upstream, midstream, downstream and petrochemical industries). However, nearly all of the book can be used in most industries, the “oil” theme being mainly on the examples of use provided. The chapters are grouped in five sections, which are given below.

1) Fundamentals are given in Chapters 1, 2 and 3. Definitions as well as mathematics are kept at the minimum vital. However, the meaning and the validity of the bathtub curve and of the early life period are provided with details in Chapter 1. Nearly all of the mathematics used in this book is given in Chapter 2. Although it is uncommon to do a reliability calculation without a standard laptop computer, basic formulae as well as the availability and reliability of standard systems are given in Chapter 3. These formulae are to be considered as a tool for orientating and validating (as far as possible) complex calculations.
2) Modeling techniques are provided in Chapters 4 and 5 and Appendix 2. Failure mode and effects analysis, reliability block diagrams, fault trees and Monte Carlo simulation are described in Chapter 4, but Chapter 5 is dedicated to Petri nets that are not used so much in the oil and gas industry¹. Markov chains are given in Appendix 2 as they are not used to assess production availability or reliability parameters in the oil and gas industry.
3) Chapters 6, 7 and 8 explain the ways to obtain reliability data. It is uncommon to devote three chapters to reliability data (one on reliability data sources, one on methods for obtaining data from reliability tests and field and one on the use of expert judgment) but the rest of the book is meaningless without them.
4) Techniques that can be considered as a support to the others in the book are in Chapter 9. As the limit to high levels of reliability is a common cause of failure, their origin and the existing methods of analysis are presented and a review of existing data sources performed. However, a major theme, “the human factor”, is considered quite briefly as the validity of existing human error quantification methods and data has not been proved in the oil and gas industry. Review of reliability engineering of electronics items and reliability engineering of mechanical pieces are the other topics considered.
5) The assessment of system production availability and system reliability characteristics and their management are explained in Chapters 10, 11 and 12. These chapters provide not only recommendations and case studies but also answers to questions such as “what we can expect from these studies, when to do them, how to perform them, how to specify them, how to include them within the plant life”. Chapter 12 on management is not only the last chapter of the book but rather it is the one binding all of the others.

As the literature in reliability engineering is large, the references given allow the reader to go deeper into several topics. An extensive use of standards is made as their number and their quality improved drastically over last 10 years.

In any industry, production availability and reliability studies are too often considered as “nice to have”, aiming at demonstrating that contractual requirements are met. A way of preventing the occurrence of this deviation (source of waste of time and money) is to organize the collaboration of reliability technicians and oil and gas professionals all along the life of the project, as well as the use of up-to-date input data and the best modeling techniques. As such, the intended audiences for this book would be as follows:

1) Oil and gas practicing engineers who do not perform any production availability or reliability assessment but want to understand the available techniques, to know the data sources and the results to expect from such assessments. Chapters 7, 8 and 9 (except common cause failures) can be skipped for that purpose.
2) Experienced reliability analysts in such assessments seeking to extend their range of expertise. The reading of Chapters 2 (apart from section 2.9 on Bayesian reliability), 3, 4 and 7 is unlikely to participate in this extension.
3) Oil and gas managers wanting to understand the benefits of these assessments and the way to use them efficiently. Chapters 1, 10, 11 and 12 are to be read in full for that purpose.
4) Students in availability and reliability wanting to improve their knowledge in production availability and reliability and to apply them to a specific industrial sector. For that purpose, Chapters 6 and 12 can be skipped.

In addition, comments are provided in the introduction of each chapter to render the reading easier for each of these populations.

Although the book was designed to be easy to read, a rigorous approach was used for any subject. As such, mathematics is used extensively even for the definitions of terms.

I would like to thank my reviewers Brian Monty, Denis Berthelot and Frederic Doux, for their invaluable help.

Alain LEROY
February 2018

Use in the Oil and Gas Industry