System Reliability Theory E-Book

Marvin Rausand

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Probability and Statistics
• Sprache: Englisch

Seitenzahl: 1191

Veröffentlichungsjahr: 2020

Beschreibung

Handbook and reference for industrial statisticians and system reliability engineers System Reliability Theory: Models, Statistical Methods, and Applications, Third Edition presents an updated and revised look at system reliability theory, modeling, and analytical methods. The new edition is based on feedback to the second edition from numerous students, professors, researchers, and industries around the world. New sections and chapters are added together with new real-world industry examples, and standards and problems are revised and updated. System Reliability Theory covers a broad and deep array of system reliability topics, including: · In depth discussion of failures and failure modes · The main system reliability assessment methods · Common-cause failure modeling · Deterioration modeling · Maintenance modeling and assessment using Python code · Bayesian probability and methods · Life data analysis using R Perfect for undergraduate and graduate students taking courses in reliability engineering, this book also serves as a reference and resource for practicing statisticians and engineers. Throughout, the book has a practical focus, incorporating industry feedback and real-world industry problems and examples.

Leseprobe

Table of Contents

Cover

Wiley Series in Probability and Statistics

System Reliability Theory

Copyright

dedication-page

Preface

Main Changes from the Second Edition

Supplementary Information on the Internet

Intended Audience

Aims and Delimitation

Authors

Acknowledgments

References

About the Companion Website

Open Site

Instructor Site

GitHub Site

Contact Person

1 Introduction

1.1 What is Reliability?

1.2 The Importance of Reliability

1.3 Basic Reliability Concepts

1.4 Reliability Metrics

1.5 Approaches to Reliability Analysis

1.6 Reliability Engineering

1.7 Objectives, Scope, and Delimitations of the Book

1.8 Trends and Challenges

1.9 Standards and Guidelines

1.10 History of System Reliability

1.11 Problems

References

2 The Study Object and its Functions

2.1 Introduction

2.2 System and System Elements

2.3 Boundary Conditions

2.4 Operating Context

2.5 Functions and Performance Requirements

2.6 System Analysis

2.7 Simple, Complicated, and Complex Systems

2.8 System Structure Modeling

2.9 Problems

References

Chapter 3: Failures and Faults

3.1 Introduction

3.2 Failures

3.3 Faults

3.4 Failure Modes

3.5 Failure Causes and Effects

3.6 Classification of Failures and Failure Modes

3.8 Problems

References

Chapter 4: Qualitative System Reliability Analysis

4.1 Introduction

4.2 FMEA/FMECA

4.3 Fault Tree Analysis

4.4 Event Tree Analysis

4.5 Fault Trees versus Reliability Block Diagrams

4.6 Structure Function

4.7 System Structure Analysis

4.8 Bayesian Networks

4.9 Problems

References

5 Probability Distributions in Reliability Analysis

5.1 Introduction

5.2 A Dataset

5.3 General Characteristics of Time‐to‐Failure Distributions

5.4 Some Time‐to‐Failure Distributions

5.5 Extreme Value Distributions

5.6 Time‐to‐Failure Models With Covariates

5.7 Additional Continuous Distributions

5.8 Discrete Distributions

5.9 Classes of Time‐to‐Failure Distributions

5.10 Summary of Time‐to‐Failure Distributions

5.11 Problems

References

6 System Reliability Analysis

6.1 Introduction

6.2 System Reliability

6.3 Nonrepairable Systems

6.4 Standby Redundancy

6.5 Single Repairable Items

6.6 Availability of Repairable Systems

6.7 Quantitative Fault Tree Analysis

6.8 Event Tree Analysis

6.9 Bayesian Networks

6.10 Monte Carlo Simulation

6.11 Problems

References

7 Reliability Importance Metrics

7.1 Introduction

7.2 Critical Components

7.3 Birnbaum's Metric for Structural Importance

7.4 Birnbaum's Metric of Reliability Importance

7.5 Improvement Potential

7.6 Criticality Importance

7.7 Fussell–Vesely's Metric

7.8 Differential Importance Metric

7.9 Importance Metrics for Safety Features

7.10 Barlow–Proschan's Metric

7.11 Problems

References

8 Dependent Failures

8.1 Introduction

8.2 Types of Dependence

8.3 Cascading Failures

8.4 Common‐Cause Failures

8.5 CCF Models and Analysis

8.6 Basic Parameter Model

8.7 Beta‐Factor Model

8.8 Multi‐parameter Models

8.9 Problems

References

9 Maintenance and Maintenance Strategies

9.1 Introduction

9.2 Maintainability

9.3 Maintenance Categories

9.4 Maintenance Downtime

9.5 Reliability Centered Maintenance

9.6 Total Productive Maintenance

9.7 Problems

References

10 Counting Processes

10.1 Introduction

10.2 Homogeneous Poisson Processes

10.3 Renewal Processes

10.4 Nonhomogeneous Poisson Processes

10.5 Imperfect Repair Processes

10.6 Model Selection

10.7 Problems

References

11 Markov Analysis

11.1 Introduction

11.2 Markov Processes

11.3 Asymptotic Solution

11.4 Parallel and Series Structures

11.5 Mean Time to First System Failure

11.6 Systems with Dependent Components

11.7 Standby Systems

11.8 Markov Analysis in Fault Tree Analysis

11.9 Time‐Dependent Solution

11.10 Semi‐Markov Processes

11.11 Multiphase Markov Processes

11.12 Piecewise Deterministic Markov Processes

11.13 Simulation of a Markov Process

11.14 Problems

References

12 Preventive Maintenance

12.1 Introduction

12.2 Terminology and Cost Function

12.3 Time‐Based Preventive Maintenance

12.4 Degradation Models

12.5 Condition‐Based Maintenance

12.6 Maintenance of Multi‐Item Systems

12.7 Problems

References

Chapter 13: Reliability of Safety Systems

13.1 Introduction

13.2 Safety‐Instrumented Systems

13.3 Probability of Failure on Demand

13.4 Safety Unavailability

13.5 Common Cause Failures

13.6 CCFs Between Groups and Subsystems

13.7 IEC 61508

13.8 The PDS Method

13.9 Markov Approach

13.10 Problems

References

14 Reliability Data Analysis

14.1 Introduction

14.2 Some Basic Concepts

14.3 Exploratory Data Analysis

14.4 Parameter Estimation

14.5 The Kaplan–Meier Estimate

14.6 Cumulative Failure Rate Plots

14.7 Total‐Time‐on‐Test Plotting

14.8 Survival Analysis with Covariates

14.9 Problems

References

15 Bayesian Reliability Analysis

15.1 Introduction

15.2 Bayesian Data Analysis

15.3 Selection of Prior Distribution

15.4 Bayesian Estimation

15.5 Predictive Distribution

15.6 Models with Multiple Parameters

15.7 Bayesian Analysis with R

15.8 Problems

References

16 Reliability Data: Sources and Quality

16.1 Introduction

16.2 Generic Reliability Databases

16.3 Reliability Prediction

16.4 Common Cause Failure Data

16.5 Data Analysis and Data Quality

16.6 Data Dossier

References

Appendix A: Appendix AAcronyms

Appendix B: Appendix BLaplace Transforms

B.1 Important Properties of Laplace Transforms

B.2 Laplace Transforms of Some Selected Functions

Author Index

Subject Index

Wiley Series in Probability and Statistics

End User License Agreement

List of Tables

Chapter 1

Table 1.1 Availability and downtime.

Chapter 4

Table 4.1 Deductive versus inductive methods.

Table 4.2 Occurrence rating (example).

Table 4.3 Severity rating (example).

Table 4.4 Fault tree symbols.

Table 4.5 Criticality ranking of minimal cut sets of order 2.

Table 4.6 Truth table for a 2oo3 structure.

Table 4.7 Truth table for a series structure of two components.

Table 4.8 Truth table for a parallel structure of two components.

Table 4.9 Truth table for the 2oo3 structure.

Chapter 5

Table 5.1 Historical dataset.

Table 5.2 Relationship between the functions

, and

.

Table 5.3 Summary of time‐to‐failure distributions and parameters.

Chapter 6

Table 6.1 A brief comparison of the structures (1), (2), and (3).

Table 6.2 MTTF of some

oo

structures of identical and independent components...

Table 6.3 Prior probability of root node

.

Table 6.4 Conditional probability table for two nodes.

Table 6.5 Prior probability of the root nodes

and

.

Table 6.6 Table for Problem 

6.10

.

Chapter 7

Table 7.1 Critical path vectors for component 1.

Chapter 10

Table 10.1 Failure times (operating days) in chronological order.

Table 10.2 Data set for Problem 13.

Chapter 11

Table 11.1 Possible states of a structure of two components.

Table 11.2 Possible states of a series structure of two components where fail...

Table 11.3 The possible states of a two‐item parallel system with cold standb...

Chapter 13

Table 13.1 PFD of some

oo

structures of identical and independent components...

Table 13.2 PFD and spurious trip rate for three simple structures.

Table 13.3 Safety integrity levels for safety functions.

Table 13.4 Failure rates for the “fail to function” mode.

Chapter 14

Table 14.1 A complete and ordered dataset of survival times.

Table 14.2 Computation of the Kaplan–Meier Estimate (censored times are marke...

Table 14.3 The Kaplan–Meier estimate as a function of time.

Table 14.4 Nelson–Aalen estimate for the censored dataset in Example 14.12, c...

Table 14.5 TTT Estimates for the dataset in Example 14.15.

Table 14.6 Dataset for Problem 14.2.

Table 14.7 Dataset for Problem 14.3.

Table 14.8 Dataset for Problem 14.11.

Table 14.9 Dataset for Problem 14.12.

Table 14.10 Dataset for Problem 14.13.

Table 14.11 Dataset for Problem 14.16.

Table 14.12 Dataset for Problem 14.17.

Table 14.13 Dataset for Problem 14.18.

Chapter 16

Table 16.1 Pumps, subdivision in maintainable items in OREDA.

2

Table B.1 Some main properties of Laplace transforms.

Table B.2 Some Laplace transforms.

List of Illustrations

Chapter 1

Figure 1.1 The reliability concept.

Figure 1.2 Main drivers for high reliability.

Figure 1.3 Main steps of risk analysis, with main methods. The methods cover...

Figure 1.4 Reliability as basis of other applications.

Figure 1.5 Load and the strength distributions at a specified time

.

Figure 1.6 Possible realization of the load and the strength of an item.

Figure 1.7 The system reliability analysis process.

Figure 1.8 The phases of a system development project (example).

Figure 1.9 Factors that influence item requirements.

Chapter 2

Figure 2.1 System breakdown structure (simplified).

Figure 2.2 A study object (system) and its boundary.

Figure 2.3 A function illustrated as a functional block.

Figure 2.4 Function tree (generic).

Figure 2.5 SADT diagram for subsea oil and gas stimulation.

Figure 2.6 Top‐down approach to establish an SADT model.

Figure 2.7 System analysis and synthesis.

Figure 2.8 Component function

shown as a block.

Figure 2.9 Alternative representation of the block in Figure 2.8

Figure 2.10 A simple reliability block diagram with three blocks.

Figure 2.11 An alternative, and identical, version of the RBD in Figure 2.10...

Figure 2.12 RBD for a series structure.

Figure 2.13 Parallel structure.

Figure 2.14 Voted structure 2oo3, (left) a physical diagram and (right) an R...

Figure 2.15 Standby structure.

Figure 2.16 RBD for a series–parallel structure.

Figure 2.17 Two safety valves in a pipeline: (a) physical layout, (b) RBD fo...

Figure 2.18 Construction of the RBD in levels.

Chapter 3

Figure 3.1 States and transitions for a safety valve.

Figure 3.2 Failure as a transition from a functioning state to a failed stat...

Figure 3.3 Illustration of the difference between failure and fault for a de...

Figure 3.4 Doorbell and associated circuitry.

Figure 3.5 Relation between failure causes, failure modes, and failure effec...

Figure 3.6 Relationship between failure cause, failure mode, and failure eff...

Figure 3.7 Failure classification..

Figure 3.8 A primary failure leading to an item fault.

Figure 3.9 A secondary failure, caused by an overstress event, leading to an...

Figure 3.10 A systematic fault leading to a systematic failure.

Figure 3.11 The structure of a security failure.

Figure 3.12 Failure causes and mechanisms. A failure mechanism is a specific...

Figure 3.13 Cause and effect diagram for the event “car will not start.”

Figure 3.14 Repeatedly asking why?

Chapter 4

Figure 4.1 Deductive versus inductive analysis of a fault or deviation in th...

Figure 4.2 Timeline of the development of FMECA variants (not in scale).

Figure 4.3 The mains steps of FMECA.

Figure 4.4 Example of an FMECA worksheet.

Figure 4.5 Risk matrix of the different failure modes.

Figure 4.6 A simple fault tree.

Figure 4.7 System overview of fire detector system.

Figure 4.8 Schematic layout of the fire detector system.

Figure 4.9 Fault tree for the fire detector system in Example 4.1.

Figure 4.10 Example of a fault tree.

Figure 4.11 Sketch of a first stage gas separator.

Figure 4.12 Fault tree for the first stage separator in Example 4.2.

Figure 4.13 A simple event tree for a dust explosion.

Figure 4.14 Presentation of results from ETA.

Figure 4.15 Activation pressures for the three protection layers of the proc...

Figure 4.16 An event tree for the initiating event “blockage of the gas outl...

Figure 4.17 Relationship between some simple RBDs and fault trees.

Figure 4.18 RBD for the fire detector system.

Figure 4.19 Component 2 is irrelevant.

Figure 4.20 Example structure.

Figure 4.21 Redundancy at system level.

Figure 4.22 Redundancy at component level.

Figure 4.23 Bridge structure.

Figure 4.24 2oo3 structure represented as a series structure of the minimal ...

Figure 4.25 The bridge structure represented as a parallel structure of the ...

Figure 4.26 The bridge structure represented as a series structure of the mi...

Figure 4.27 The structure

of the bridge structure.

Figure 4.28 The structure

of the bridge structure.

Figure 4.29 RBD.

Figure 4.30 Structure of modules.

Figure 4.31 The three substructures.

Figure 4.32 Module II.

Figure 4.33 Two prime modules.

Figure 4.34 The main BN symbols.

Figure 4.35 (a) Linear, (b) converging, and (c) diverging BN with three node...

Figure 4.36 BN for a system

of two independent components

and

.

Figure 4.37 BN for a 2oo3 structure

of three components

,

, and

.

Figure 4.38 A simple fault tree and the corresponding BN.

Figure 4.39 Hydraulically operated gate valve (Problem 4.2).

Figure 4.40 RBD for Problem 4.4.

Figure 4.41 RBD for Problem 4.6.

Figure 4.42 Lubrication system on a ship engine (Problem 4.7).

Figure 4.43 RBD for Problem 4.11.

Figure 4.44 Fault tree for Problem 4.12.

Figure 4.45 RBD for Problem 12.

Figure 4.46 RBD for Problem 4.13.

Figure 4.47 RBD for Problem 4.14.

Chapter 5

Figure 5.1 The state variable and the time‐to‐failure of an item.

Figure 5.2 Relative frequency distribution (histogram) (a) and empirical sur...

Figure 5.3 Probability density function,

for the time‐to‐failure

.

Figure 5.4 The distribution function

(fully drawn line) together with the ...

Figure 5.5 Illustration of the integral calculation of the probability to fa...

Figure 5.6 The survivor function

.

Figure 5.7 Empirical bathtub curve.

Figure 5.8 The bathtub curve.

Figure 5.9 Location of the MTTF, the median lifetime, and the mode of a dist...

Figure 5.10 The survivor function

, the probability density function

, and...

Figure 5.11 The residual lifetime of an item that is still functioning at ti...

Figure 5.12 The survivor function

(fully drawn line), the conditional surv...

Figure 5.13 The

function (5.38) in Example 5.2.

Figure 5.14 Probability density function

(fully drawn line) and distributi...

Figure 5.15 The failure rate function of the mixture of two exponential dist...

Figure 5.16 The failure rate function of an item with stepwise constant fail...

Figure 5.17 The gamma probability density for selected values of

,

.

Figure 5.18 Survivor function for the gamma distribution for selected values...

Figure 5.19 Failure rate function of the gamma distribution for selected val...

Figure 5.20 The probability density function of the Weibull distribution for...

Figure 5.21 Failure rate function of the Weibull distribution,

and four di...

Figure 5.22 The proportionality factor of MTTF as a function of

.

Figure 5.23 The scaled mean residual lifetime function

MRL

/MTTF for the W...

Figure 5.24

as a function of

, the number of independent and identical co...

Figure 5.25 The normal distribution with mean

and standard deviation

.

Figure 5.26 Failure rate function of the standard normal distribution wit me...

Figure 5.27 Probability density of the lognormal distribution with

and

. ...

Figure 5.28 Failure rate function of the lognormal distribution with

and

Figure 5.29 Wöhler or

–

diagram.

Figure 5.30 The probability density of

.

Figure 5.31 The probability density of

for some selected values of

and

Figure 5.32 The binomial distribution (

).

Figure 5.33 Probability density (Problem 

5.19

5.19).

Chapter 6

Figure 6.1 RBD of a simplified automatic alarm system for gas leakage.

Figure 6.2 The failure rate function of a series structure of three independ...

Figure 6.3 Transition diagram for a parallel structure of

independent and ...

Figure 6.4 The probability density function of a parallel structure with two...

Figure 6.5 The failure rate for a parallel structure of two independent comp...

Figure 6.6 Failure rate function for a parallel structure of two independent...

Figure 6.7 The failure rate function

for a 2oo3 structure of independent a...

Figure 6.8 The survivor functions of the three structures in Table 6.1 (

)....

Figure 6.9 Standby system with

items.

Figure 6.10 Standby system with 2 items.

Figure 6.11 States of a repairable item.

Figure 6.12 The availability

of an item with failure rate

and repair rat...

Figure 6.13 RBD for Example 6.16.

Figure 6.14 RBD for Example 6.20, drawn as a series structure of its three M...

Figure 6.15 State variables for fault tree

AND

and

OR

gates.

Figure 6.16 Fault trees with single

AND

‐gate and single

OR

‐gate.

Figure 6.17 A structure represented as a series structure of the minimal cut...

Figure 6.18 RBD for the bridge structure.

Figure 6.19 BDD deduced from a truth table.

Figure 6.20 Simple BN with two nodes.

Figure 6.21 Linear BN with three nodes.

Figure 6.22 BN with Three Nodes.

Figure 6.23 BN for a simple system of two components.

Figure 6.24 Generation of a random variable with distribution

.

Figure 6.25 System of two production items.

Figure 6.26 Simulation of the performance of the production system in Figure...

Figure 6.27 RBD for Problem 

6.7

6.7.

Figure 6.28 Fault tree for Problem 

6.9

9.

Chapter 7

Figure 7.1 Simple system of three components.

Figure 7.2 Illustration of Birnbaum's metric of reliability importance.

Figure 7.3 Structure with three components: RBD and associated fault tree re...

Figure 7.4 RBD (Problem 3).

Figure 7.5 RBD (Problem 6).

Chapter 8

Figure 8.1 Relationship between independent failures and CCFs of a structure...

Figure 8.2 A shared cause combined with coupling factors lead to CCF of a pa...

Figure 8.3 Explicit modeling of a CCF in a system of two pressure switches....

Figure 8.4 Probabilities of different multiplicities for a voted group of th...

Figure 8.5 A component represented as a series structure of two blocks.

Figure 8.6 A parallel structure modeled by the beta‐factor model.

Figure 8.7 Fractions of different types of failures for a structure of two c...

Figure 8.8 RBD for a 2oo3:G structure modeled by the beta‐factor model.

Figure 8.9 The MTTF of a 2oo3:G structure modeled as a function of the beta‐...

Figure 8.10 Fractions of different types of failures for a system with three...

Figure 8.11 Probabilities of failures with different multiplicities.

Chapter 9

Figure 9.1 Classification of maintenance types.

Figure 9.2 Average “behavior” of a repairable item and main time concepts.

Figure 9.3 Functional failure analysis (FFA) worksheet.

Figure 9.4 RCM‐FMECA worksheet.

Figure 9.5 Maintenance task assignment/decision logic.

Figure 9.6 Time concepts used in Total productive maintenance.

Chapter 10

Figure 10.1 Relation between the number of events

, the interoccurrence tim...

Figure 10.2 The dataset in Example 10.1.

Figure 10.3 Number of failures

as a function of time for the data in Examp...

Figure 10.4 Number of critical compressor failures

as a function of time (...

Figure 10.5 The forward recurrence time

.

Figure 10.6 Types of repair and stochastic point processes covered in this b...

Figure 10.7 Number of renewals

as a function of

for a simulated renewal ...

Figure 10.8 Illustration of the conditional ROCOF (fully drawn line) for sim...

Figure 10.9 Renewal density

(fully drawn line) and renewal function

(dot...

Figure 10.10 The renewal function for Weibull distributed renewal periods wi...

Figure 10.11 The age

and the remaining lifetime

.

Figure 10.12 The renewal function

of a renewal process with underlying dis...

Figure 10.13 Superimposed renewal process.

Figure 10.14 Superimposed renewal process. Conditional ROCOF

of a series s...

Figure 10.15 Alternating renewal process.

Figure 10.16 Availability of an item with exponential up‐ and downtimes.

Figure 10.17 The availability of an item with exponential uptimes and consta...

Figure 10.18 The ROCOF

of an NHPP and random failure times.

Figure 10.19 An illustration of a possible shape of the conditional ROCOF of...

Figure 10.20 The conditional ROCOF of Chan and Shaw's proportional reduction...

Figure 10.21 The

model for some possible failure times. The “underlying” R...

Figure 10.22 Illustration of the transformation of a TRP(

) to a renewal pro...

Figure 10.23 Illustration of the conditional ROCOF

in Example 10.19 for so...

Figure 10.24 Model selection framework.

Chapter 11

Figure 11.1 Trajectory of a Markov process.

Figure 11.2 State transition diagram of the parallel structure in Example 11...

Figure 11.3 State transition diagram for the parallel structure in Example 1...

Figure 11.4 State transition diagram for a homogeneous Poisson process (HPP)...

Figure 11.5 State transition diagram for a single component (function‐repair...

Figure 11.6 Availability and survivor function for a single component (

,

)...

Figure 11.7 State transition diagram of the generators in Example 11.6.

Figure 11.8 Partitioning the state transition diagram of a series structure ...

Figure 11.9 State transition diagram of a series structure of two components...

Figure 11.10 State transition diagram for a parallel structure of two identi...

Figure 11.11 State transition diagram for a parallel structure of two compon...

Figure 11.12 The

of a parallel structure as a function of the common‐cause...

Figure 11.13 Parallel structure of two components sharing a common load.

Figure 11.14 State transition diagram for the generator system with load‐sha...

Figure 11.15 Two‐item standby system.

Figure 11.16 State transition diagram of a two‐item parallel structure with ...

Figure 11.17 State transition diagram of a two‐item parallel structure with ...

Figure 11.18 State transition diagram of a two‐item parallel structure with ...

Figure 11.19 State transition diagram of a two‐item parallel structure with ...

Figure 11.20 Reliability block diagram (a) and state transition diagram (b) ...

Figure 11.21 Example of a Markov's chain simulation – single history.

Figure 11.22 Example of a Markov's chain simulation – estimate of MTTF and s...

Figure 11.23 RBD for the pitch system in Problem 11.4.

Figure 11.24 RBD for the system in Problem 11.5.

Chapter 12

Figure 12.1 Age replacement strategy and costs.

Figure 12.2 The ratio

as a function of

for the Weibull distribution with...

Figure 12.3 The optimal replacement interval

in Example 12.2 as a function...

Figure 12.4 The average cost per time unit for a block replacement strategy ...

Figure 12.5 The average cost per time unit for a block replacement strategy ...

Figure 12.6 Average behavior and concepts used in

–

interval models.

Figure 12.7 The asymptotic cost

per time unit as a function of

for

,

...

Figure 12.8 Comparison between four different (non‐CBM) maintenance strategi...

Figure 12.9 State transition diagram for a single item with degraded states....

Figure 12.10 State transition diagram for a single item with degraded states...

Figure 12.11 State transition diagram for a single component with degraded s...

Figure 12.12 RBD of a safety‐instrumented system (SIS).

Chapter 13

Figure 13.1 Sketch of a simple SIS.

Figure 13.2 Failure mode classification.

Figure 13.3 The state

of a periodically tested item with respect to DU fai...

Figure 13.4 The safety unavailability

of a periodically tested item.

Figure 13.5 PFD

of a parallel structure of two items with staggered testing...

Figure 13.6 Contributions to safety unavailability.

Figure 13.7 Critical situation – fire detector system.

is the state of the...

Figure 13.8 A 2oo3:G sensor system.

Figure 13.9 A process shutdown valve with fail‐safe hydraulic actuator.

Figure 13.10 Explicit modeling of a CCF for a system with two pressure senso...

Figure 13.11 State transition diagram for the failure process described by H...

Figure 13.12 Smoke detector system (simplified).

Figure 13.13 Sketch of an emergency shutdown system.

Chapter 14

Figure 14.1 Main concepts of statistical inference.

Figure 14.2 Time‐to‐failure and Observed Survival Time.

Figure 14.3 An observed dataset (a), and the same dataset shifted to time 0 ...

Figure 14.4 Typical dataset for field data.

Figure 14.5 Histogram of the dataset in Table 14.1 with different numbers of...

Figure 14.6 A sample density plot of the dataset in Table 14.1.

Figure 14.7 Empirical survivor function (survival curve) for the dataset in ...

Figure 14.8 Empirical survivor function (survival curve) for the dataset in ...

Figure 14.9 Normal Q–Q plot for the dataset in Table 14.1, made with the

R

f...

Figure 14.10 Exponential Q–Q plot for the dataset in Table 14.1, made with t...

Figure 14.11 Likelihood function for the binomial distribution (

and

).

Figure 14.12 The negative log‐likelihood function for the binomial distribut...

Figure 14.13 Likelihood function for the exponential distribution in Example...

Figure 14.14 Output from a simple script using WeibullR.

Figure 14.15 Kaplan–Meier plot for the data in Example 14.9. Made with

R

.

Figure 14.16 Kaplan–Meier plot of the dataset in Example 14.9 with 90% confi...

Figure 14.17 Nelson–Aalen plot (linear scale).

Figure 14.18 Nelson–Aalen plot (log 10 scale).

Figure 14.19 TTT plot of the data in Example 14.13.

Figure 14.20 The TTT transform of the distribution

.

Figure 14.21 Scaled TTT transform of the exponential distribution (Example 1...

Figure 14.22 Scaled TTT transforms of the Weibull distribution for some sele...

Figure 14.23 TTT plots indicating (a) increasing failure rate (IFR), (b) dec...

Figure 14.24 TTT plot of the ball bearing data in Example 11.11 together wit...

Figure 14.25 Determination of the optimal replacement age from the scaled TT...

Figure 14.26 Determination of the optimal replacement age from a TTT plot.

Figure 14.27 Failure rate function for the PH model. The baseline failure ra...

Chapter 15

Figure 15.1 The frequentist data analysis process.

Figure 15.2 The Bayesian data analysis process.

Figure 15.3 Prior beta density with parameters

and

.

Figure 15.4 The gamma distribution with parameters

and

.

Figure 15.5 Loss function.

Chapter 16

Figure 16.1 Pumps, boundary definition in OREDA.

Figure 16.2 Reliability prediction timeline.

Figure 16.3 Estimates from field data sources.

Figure 16.4 The real failure rate and the erroneously estimated constant fai...

Figure 16.5 Average failure rates estimated in two different observation win...

Figure 16.6 Estimates and confidence intervals for inhomogeneous samples.

Figure 16.7 Example of a reliability data dossier.

Guide

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Wiley Series in Probability and Statistics

Established by WALTER A. SHEWHART and SAMUEL S. WILKS

Editors

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Editors Emeriti

Vic Barnett, Ralph A. Bradley, J. Stuart Hunter, J.B. Kadane, David G. Kendall, and Jozef L. Teugels

A complete list of the titles in this series appears at the end of this volume.

System Reliability Theory

Models, Statistical Methods, and Applications

Third Edition

Marvin RausandNorwegian University of Science & TechnologyTrondheim, Norway

Anne BarrosCentraleSupélec, Paris-Saclay UniversityParis, France

Arnljot Høyland†Norwegian University of Science & TechnologyTrondheim, Norway

This third edition first published 2021

© 2021 John Wiley & Sons, Inc.

Edition History

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Library of Congress Cataloging‐in‐Publication Data

Names: Rausand, Marvin, author. | Barros, Anne, author. | Høyland, Arnljot,

 1924‐ author.

Title: System reliability theory : models, statistical methods, and

 applications / Marvin Rausand, Norwegian University of Science &

 Technology, Trondheim, Norway, Anne Barros, CentraleSupélec, Paris‐Saclay University,

 Paris, France, Arnljot Høyland, Norwegian

 University of Science & Technology, Trondheim, Norway.

Description: Third edition. | Hoboken, NJ : John Wiley & Sons, Inc., 2021.

 | Series: Wiley series in probability and statistics | Includes

 bibliographical references and index.

Identifiers: LCCN 2020016182 (print) | LCCN 2020016183 (ebook) | ISBN

 9781119373520 (cloth) | ISBN 9781119374015 (adobe pdf) | ISBN

 9781119373957 (epub)

Subjects: LCSH: Reliability (Engineering)–Statistical methods.

Classification: LCC TA169 .H68 2021 (print) | LCC TA169 (ebook) | DDC

 620/.00452–dc23

LC record available at https://lccn.loc.gov/2020016182

LC ebook record available at https://lccn.loc.gov/2020016183

Cover Design: Wiley

Cover Images: System reliability theory Courtesy of Marvin Rausand,

Abstract purple and pink polygonal © Tuomas Lehtinen/Getty Images

To Hella; Guro and Idunn; and Emil and Tiril

To: Nicolas; Penelope; and Garance

Preface

This book provides a basic, but rather comprehensive introduction to system reliability theory and the main methods used in reliability analyses. System reliability theory is used in many application areas. Some of these are illustrated in the book as examples and problems.

Main Changes from the Second Edition

Readers who are familiar with the second edition (Rausand and Høyland 2004) will find that the third edition is a major update and that most chapters have been rewritten. The most significant changes include:

A new

Chapter 2

defining the study object and its functions and operating context is included. System modeling by reliability block diagrams is introduced and the concept of complexity is discussed.

A new

Chapter 3

defining and discussing the concepts of failure and fault, together with several associated concepts is added. Two failure analysis techniques are presented.

New component importance metrics are included.

The treatment of dependent failures is significantly extended.

Section 8.8 on complex systems in the second edition is removed from the chapter on Markov analysis where several new models are added.

A new

Chapter 2

on preventive maintenance is added. This chapter merges aspects from the previous edition with new models and methods. The presentation is supplemented by Python scripts that are found on the

book companion site

.

Chapters 11

and

13

in the second edition on life data analysis and Bayesian reliability analysis are totally rewritten. The statistical program system

R

is extensively used in the presentation.

Chapter 12

in the second edition on accelerated testing has been removed, but parts of the chapter are moved to the chapter on reliability data analysis.

The end of chapter problems have been revised and new problems are added.

Most of the appendices are removed. The content is partly integrated in the text and partly obsolete because of the use of

R

.

An author index is provided.

Supplementary Information on the Internet

An immense amount of relevant information is today available on the Internet, and many of the topics in this book may be found as books, reports, lecture notes, or slides written by lecturers from many different universities. The quality of this information is varying and ranging from very high to rather low, the terminology is often not consistent, and it may sometimes be a challenge to read some of these Internet resources. The reader is encouraged to search the Internet for alternative presentations and compare with the book. This way, new ideas and increased insight may spring up.

With the abundance of free information on the Internet, it is pertinent to ask whether a traditional book is really needed. We strongly believe that a book may provide a more coherent knowledge and we have tried to write the book with this in mind.

Intended Audience

The book is written primarily for engineers and engineering students, and the examples and applications are related to technical systems. There are three groups that constitute our primary audience:

The book was originally written as a textbook for university courses in system reliability at the Norwegian University of Science and Technology (NTNU) in Trondheim. This third edition is based on experience gained from use of the first two editions, at NTNU and many other universities, and also from using the book in a wide range of short courses for industry.

The second is to be a guide for engineers and consultants who carry out practical system reliability analyses of technical systems.

The third is to be a guide for engineers and consultants in areas where reliability is an important aspect. Such areas include risk assessment, systems engineering, maintenance planning and optimization, logistics, warranty engineering and management, life cycle costing, quality engineering, and several more. It may be noted that several of the methods used in artificial intelligence and machine learning are treated in this book.

Readers should have a basic course in probability theory. If not, you should get hold of an introductory textbook in probability and statistics to study in parallel with reading this book. A multitude of relevant lecture notes, slides, and reports are also available on the Internet. Brief guidance to relevant sources is provided on the book companion site.

Aims and Delimitation

The book is intended to give a thorough introduction to system reliability. Detailed objectives and associated delimitations are found in Section 1.8. The study object may range from a single component up to a rather complicated technical system. The study object is delimited to items that are mainly based on mechanical, electrical, or electronic technology. An increasing number of modern items have a lot of embedded software. Functions that earlier were carried out by mechanical and electromechanical technology are today software‐based functions. A family car that was built when the second edition was published is, for example, very different from a modern car, which is sometimes characterized as a “computer on wheels.” Software reliability is different from hardware reliability in many ways and we, therefore, consider pure software reliability to be outside the scope of the book. Many software‐based functions may, however, be treated with the methods presented.

Many modern systems are getting more and more complex. Chapter 2 introduces three categories of systems: simple, complicated, and complex systems. Complex systems are here defined to be systems that do not meet all the requirements of the Newtonian–Cartesian paradigm and therefore cannot be adequately analyzed with traditional methods. The complexity theory and the approaches to study complex systems is considered to be outside the scope of the book.

The objective of this book is to help the reader to understand the basic theory of system reliability and to become familiar with the most commonly used analytical methods. We have focused on producing reliability results by hand‐calculation, sometimes assisted by simple R and Python programs. When you carry out practical reliability analyses of large systems, you usually need some special computer programs, such as fault tree analysis programs and simulation programs. A high number of programs are available on the market. We do not present any of these special programs in the book, but supply a list of the main vendors of such programs on the book companion site. To use a specific program, you need to study the user manual. This book should help you understand the content of such manuals and the sources of uncertainty of the results produced.

A wide range of theories and methods have been developed for system reliability analysis. All these cannot be covered in an introductory text. When selecting material to cover, we have focused on methods that:

Are commonly used in industry or in other relevant application areas

Give the analyst insights that increase her understanding of the system (such that system weaknesses can be identified at an early stage of the analysis)

Provide the analyst with genuine insight into system behavior

Can be used for hand‐calculation (at least for small systems)

Can be explained rather easily to, and be understood by nonreliability engineers and managers.

The authors have mainly been engaged in applications related to the offshore oil and gas industry and many examples therefore come from this industry. The methods described and many of the examples are equally suitable for other industries and application areas.

Authors

The first edition of the book (Høyland and Rausand 1994) was written with joint efforts from Arnljot Høyland and Marvin Rausand. Arnljot sorrily passed away in 2002. The second edition (Rausand and Høyland 2004), was therefore prepared by Marvin alone and represented a major update of the first edition. Marvin retired from his professorship at NTNU in 2015 and when Wiley wanted an updated version, he asked Anne Barros to help preparing this third edition. Due to unforeseen practical constraints, Anne could not devote as much time to this project as she wanted. Anne's contribution to this edition is mainly related to Chapters 11 and 12, the end of chapter problems, in addition to reviewing and proposing improvements to other chapters.

Acknowledgments

First of all, we express our deepest thanks to Professor Arnljot Høyland. Professor Høyland passed away in December 2002, 78 years old, and could not participate in writing any further editions of the book. We hope that he would have approved and appreciated the changes and additions we have made.

The authors sincerely thank a high number of students at NTNU, and lecturers and students at many other universities around the world for comments to the previous edition and for suggesting improvements. We have done our best to implement these suggestions. Special thanks go to Professor Bruno Castanier, Université d'Angers, for making significant contributions to Section 12.3, and to Per Hokstad, SINTEF, for many inputs to Chapter 8.

Many definitions used in the book are from, or are inspired by, the International Electrotechnical Vocabulary (IEV) www.electropedia.org. We appreciate the initiative of the International Electrotechnical Commission (IEC) to make this vocabulary freely available. References to the vocabulary are given in the text as the IEV ref. number (e.g. IEV 192‐01‐24 for the term reliability).

Last, but not least, we are grateful to the editorial and production staff at John Wiley & Sons for their careful, effective, and professional work. In particular, we would like to thank our main contacts in the final stages of preparing the book, Sarah Keegan, Kathleen Santoloci, and Viniprammia Premkumar.

Trondheim, 2020

Marvin Rausand and Anne Barros

References

Høyland, A. and Rausand, M. (1994).

System Reliability Theory: Models and Statistical Methods

. Hoboken, NJ: Wiley.

Rausand, M. and Høyland, A. (2004).

System Reliability Theory: Models, Statistical Methods, and Applications

, 2e. Hoboken, NJ: Wiley.

About the Companion Website

System Reliability Theory: Models, Statistical Methods, and Applications is accompanied by a companion website:

www.wiley.com/go/SystemReliabilityTheory3e

The book companion site is split into two sub-sites hosted by Wiley:

An

open site

that is accessible to all users of the book.

An

instructor site

for instructors/lecturers (i.e. not accessible for students and general readers of the book).

The two sites contain a number of PDF files. These files have version numbers and will be updated when required.

In addition to these two sites hosted by Wiley, we will maintain a GitHub site for the book.

Open Site

The open site contains:

A

supplement

to the book with comments to chapters, suggestions for further reading, and general information about the subject area.

Slides to the various chapters (made with LaTeX/Beamer).

Control questions to each chapter.

Errata (list of misprints and minor errors – a more frequently updated errata list may be found on the book's GitHub site).

Instructor Site

The instructor site contains:

Solutions to end of chapter problems.

Suggested lecturing plans (what to cover, which problems to use, etc.).

Additional problems with solutions.

FAQ list.

GitHub Site

The GitHub site is open to all users – and should have a clear link from the Wiley sites. The GitHub site will contain:

A brief description of the book.

Detailed R-scripts related to the book.

Detailed Python-scripts related to the book.

Errata list (see above under

Open site

).

FAQ related to the book – with our answers/comments.

The URL of the GitHub site is https://github.com/RausandBarros/ReliabilityBookScripts

Contact Person

The contact person for the book companion site and the GitHub site is Anne Barros ([email protected])

1Introduction

1.1 What is Reliability?

Nowadays, nearly all of us depend on a wide range of technical products and services in our everyday life. We expect our electrical appliances, cars, computers, mobile phones, and so on, to function when we need them, and to be reliable for a rather long time. We expect services, such as electricity, computer networks, and transport, to be supplied without disruptions or delays. When a product, machinery, or service fails, the consequences may sometimes be catastrophic. More often, product flaws and service outages lead to customer dissatisfaction and expenses for the supplier through warranty costs and product recalls. For many suppliers, reliability has become a matter of survival.

There is no generally accepted definition of the reliability of a technical product. The definition and interpretation of the term vary from industry to industry and from user to user. For the purpose of this book, we choose a rather wide definition of the reliability of a technical item.

Definition 1.1 (Reliability)

The ability of an item to perform as required in a stated operating context and for a stated period of time.

The term item is used to designate any technical system, subsystem, or component. The items studied in this book are built of hardware parts, and to an increasing degree, of software. When relevant, the user interface is part of the item, but operators and other humans are not part of the items studied here.

The reliability concept is illustrated in Figure 1.1. The required performance is determined by laws and regulations, standards, customer requirements and expectations, and supplier requirements, and is usually stated in a specification document, where delimitations of the operating context are stated. As long as the predicted performance at least fulfills the required performance, the item is reliable – when it is used in the same operating context and for the period of time stated in the required performance.

Figure 1.1 The reliability concept.

By operating context, we mean the environmental conditions the item is used in, the usage patterns, and the loads it is subjected to, and how the item is serviced and maintained.

Definition 1.1 is not new and is not created by us. Several authors and organizations have used this, or a very similar definition of reliability, at least since the 1980s. A more thorough discussion of reliability and related concepts is given in Section 1.3.

1.1.1 Service Reliability

A service is provided by a person, an organization, or a technical item to a person or a technical item. The entity providing the service is called a service provider, and the entity receiving the service is called a customer. Services can be provided on a (i) continuous basis (e.g. electric power, computer networks), (ii) according to a timetable (e.g. bus, rail, and air transport), or (iii) on demand (e.g. payment by debit cards).

Many services are provided by a single service provider to a high number of customers. A customer considers the service to be reliable when she receives the service (e.g. electric power) with sufficient quality without outages. We define service reliability as follows:

Definition 1.2 (Service reliability)

The ability of the service to meet its supply function with the required quality under stated conditions for a specified period of time.

Several quantitative service reliability metrics have been defined, but they vary between the different types of services.

1.1.2 Past and Future Reliability

In our daily language, the term “reliability” is used to describe both past and future behavior. We may, for example, say that (i) “my previous car was very reliable” and (ii) “I believe that my new car will be very reliable.” These two statements are quite different. The first statement is based on experience with the car over a certain period, whereas the second statement is a prediction of what will happen in the future. We distinguish them by using two different terms.

Reliability

(single word) is always used to describe the

future

performance of an item. Because we cannot predict the future with certainty, we need to use probabilistic statements when assessing the reliability.

Achieved reliability

is used to describe the item's

past

performance, which is assumed to be known to the analyst. No probabilistic statements are therefore involved. The achieved reliability is also called

observed reliability

.

The focus of this book is on reliability and the future performance. The achieved reliability is most relevant in Chapter 14, where analysis of observed failure data is discussed.

1.2 The Importance of Reliability

Several producers of technical items have struggled and even collapsed because of item flaws and failures. To build a reputation for reliability is a long‐term project, but it may take a short time to lose this reputation. The main drivers for high reliability are listed in Figure 1.2. Over the years, the reliability has improved for almost all types of items, but at the same time, customers expect a higher and higher reliability of the new items they buy. Current customers further expect that possible failures in the warranty period are rectified without any cost to the customer. To be attractive in the market, the suppliers have to offer a longer and longer warranty period.

Figure 1.2 Main drivers for high reliability.

If items have flaws that affect safety, safety regulations may require all the flawed items to be recalled for repair or modification. Such recalls are rather frequent in the car industry, but are also common in many other industries. In addition to excessive warranty costs and item recalls, flawed items lead to dissatisfied and nonreturning customers.

1.2.1 Related Applications

Reliability considerations and reliability studies are important inputs to a number of related applications. Several of these applications have adopted the basic terminology from reliability. Among the relevant applications are:

Risk analysis

. The main steps of a

quantitative risk analysis

(QRA) are: (i) identification and description of potential

initiating events

that may lead to unwanted consequences, (ii) identification of the main causes of each initiating event and quantification of the frequency of the initiating events, and (iii) identification of the potential consequences of the initiating events and quantification of the probabilities of each consequence. The three steps are shown in the

bow‐tie model

in

Figure 1.3

, where the main methods are indicated. The methods that are covered in this book are marked with an

.

Maintenance planning

. Maintenance and reliability are closely interlinked. High‐quality maintenance improves the operational reliability and high reliability gives few failures and low maintenance cost. The close link is also visible in the popular approach

reliability‐centered maintenance

(RCM), which is discussed in

Chapter 9

.

Quality

. Quality management is increasingly focused, stimulated by the ISO 9000 series of standards. The concepts of quality and reliability are closely connected. Reliability may in some respects be considered to be a quality characteristic.

Life cycle costing

. The life cycle cost (LCC) may be split into three types: (i) capital expenditure (CAPEX), (ii) operational expenditure (OPEX), and (iii) risk expenditure (RISKEX). The main links to reliability are with types (ii) and (iii). The OPEX is influenced by how regular the function/service is and the cost of maintenance. The RISKEX covers the cost related to accidents, system failures, and insurance. LCC is also called

total ownership cost

.