Cover

Dedication

Title Page

Copyright

Contents

Preface

Notations and Abbreviations

1. Reliability of Engineering Systems

1.1. Basic notions and characteristics of reliability

1.1.1. Basic notions

1.1.2. Reliability of non-renewable units

1.1.3. Some parametric families of continuous distributions of non-negative random variables

1.1.4. Examples

1.1.5. Exercises

1.2. Reliability of renewable systems

1.2.1. Reliability of instantaneously renewable articles

1.2.2. Renewal function

1.2.3. Age and residual lifetime of an article

1.2.4. Reliability characteristics with regard to replacement time

1.2.5. Examples

1.2.6. Exercises

1.3. Statistical analysis of reliability characteristics

1.3.1. Introductory notes

1.3.2. Observations and the plans of reliability trials

1.3.3. Statistical analysis of reliability characteristics for trials under the basic plan

1.3.4. Statistical estimation of the reliability characteristics and indexes for trials with renewable units

1.3.5. Examples

1.3.6. Exercises

1.4. Structural reliability

1.4.1. System structure function

1.4.2. Monotone structures

1.4.3. Reliability of monotone systems from independent elements

1.4.4. Reliability function for monotone structures

1.4.5. Exercises

1.5. System life tree and its structure function

1.5.1. Event tree

1.5.2. An object structure scheme

1.5.3. An example: the auto engine structure scheme

1.5.4. Life tree and the system structure function

1.5.5. Calculation of the system reliability

1.5.6. System reliability function calculation

1.6. Non-renewable redundant systems

1.6.1. Basic redundancy means – terms

1.6.2. Hot redundancy

1.6.3. Cold redundancy

1.6.4. Markov process for system reliability investigations

1.6.5. Reliability properties of redundant systems

1.6.6. A unit warranty operating time calculation

1.6.7. Exercises

1.7. Renewable redundant systems

1.7.1. The model

1.7.2. Equations for probabilities of the system states

1.7.3. Steady state probabilities: system failure probability

1.7.4. Reliability function for renewable systems

1.7.5. Exercises

1.8. Bibliographical comments

1.8.1. Section 1.1

1.8.2. Section 1.2

1.8.3. Section 1.3

1.8.4. Section 1.4

1.8.5. Section 1.5

1.8.6. Sections 1.6 and 1.7

2. Reliability and Risk

2.1. Risk: notion and measurement

2.1.1. Introductory notes

2.1.2. Examples

2.1.3. Risk notion

2.1.4. Risk measurement

2.1.5. Risk modeling

2.1.6. Exercises

2.2. Models of damage value

2.2.1. Introductory remarks

2.2.2. Simple damage models

2.2.3. Compound damages: methods of investigation

2.2.4. Moments of compound damages

2.2.5. Models of compound damages

2.2.6. Examples

2.2.7. Exercises

2.3. Methods of risk analysis

2.3.1. Introductory remarks

2.3.2. Methodology of risk analysis

2.3.3. Risk tree construction

2.3.4. Risk tree rigging

2.3.5. Risk tree analysis

2.3.6. Exercise

2.4. Bibliographical comments

2.4.1. Section 2.1

2.4.2. Section 2.2

2.4.3. Section 2.3

3. Risk Management

3.1. Insurance of risks and risk of insurance

3.1.1. Introductory remarks

3.1.2. Basic notions

3.1.3. Risk insurance models

3.1.4. Basic risk insurance problems

3.1.5. Examples

3.1.6. Exercises

3.2. Some notions and methods of financial mathematics

3.2.1. Principal notion of financial mathematics

3.2.2. Simple interests

3.2.3. Compound interests

3.2.4. Cash flows and the financial rents

3.2.5. Exercises

3.3. Short-time insurance model investigation

3.3.1. Introductory remarks

3.3.2. Calculation of the individual claim indexes

3.3.3. Exact calculation of summary claim characteristics

3.3.4. Normal asymptotic of summary claim distribution

3.3.5. Poisson asymptotic of summary claim distribution

3.3.6. Calculation of insurance basic characteristics

3.3.7. Exercises

3.4. Long-time insurance model investigation

3.4.1. Introductory remarks

3.4.2. The basic parameters of long-time insurance contracts

3.4.3. Insurance annuity analysis

3.4.4. The net-premium calculation

3.4.5. Insurance load calculation

3.4.6. An example

3.4.7. Exercises

3.5. Bibliographical comments

3.5.1. Section 3.1

3.5.2. Section 3.2

3.5.3. Sections 3.3 and 3.4

Appendices

Appendix 1: Distributions

Appendix 2: Data for Examples and Exercises

Bibliography

Index

Other titles from iSTE in Mathematics and Statistics

EULA