Reliability of Engineering Systems and Technological Risk

Vladimir Rykov is Professor in the Applied Mathematics and Computer Modeling Department of the Gubkin Russian State Oil and Gas University in Moscow. His main interests include controllable queueing systems and reliability theory.

"Although the material in this book is aimed at those working towards a bachelor's degree in engineering, it may also be of interest to postgraduate students and specialists dealing with problems related to reliability and risks." (Zentralballt MATH, 2016)

• Preface ixNotations and Abbreviations xiChapter 1. Reliability of Engineering Systems 11.1. Basic notions and characteristics of reliability 11.1.1. Basic notions 11.1.2. Reliability of non-renewable units 31.1.3. Some parametric families of continuous distributions of non-negative random variables 71.1.4. Examples 211.1.5. Exercises 231.2. Reliability of renewable systems 241.2.1. Reliability of instantaneously renewable articles 241.2.2. Renewal function 301.2.3. Age and residual lifetime of an article 341.2.4. Reliability characteristics with regard to replacement time 371.2.5. Examples 381.2.6. Exercises 431.3. Statistical analysis of reliability characteristics 441.3.1. Introductory notes 441.3.2. Observations and the plans of reliability trials 451.3.3. Statistical analysis of reliability characteristics for trials under the basic plan 461.3.4. Statistical estimation of the reliability characteristics and indexes for trials with renewable units 501.3.5. Examples 521.3.6. Exercises 541.4. Structural reliability 541.4.1. System structure function 551.4.2. Monotone structures 571.4.3. Reliability of monotone systems from independent elements 611.4.4. Reliability function for monotone structures 631.4.5. Exercises 641.5. System life tree and its structure function 681.5.1. Event tree 681.5.2. An object structure scheme 691.5.3. An example: the auto engine structure scheme 711.5.4. Life tree and the system structure function 721.5.5. Calculation of the system reliability 761.5.6. System reliability function calculation  791.6. Non-renewable redundant systems 821.6.1. Basic redundancy means – terms 821.6.2. Hot redundancy 841.6.3. Cold redundancy 851.6.4. Markov process for system reliability investigations 861.6.5. Reliability properties of redundant systems 901.6.6. A unit warranty operating time calculation 951.6.7. Exercises 961.7. Renewable redundant systems 971.7.1. The model 971.7.2. Equations for probabilities of the system states 991.7.3. Steady state probabilities: system failure probability 1001.7.4. Reliability function for renewable systems 1011.7.5. Exercises 1051.8. Bibliographical comments 1081.8.1. Section 1.1 1081.8.2. Section 1.2 1081.8.3. Section 1.3 1081.8.4. Section 1.4 1081.8.5. Section 1.5 1091.8.6. Sections 1.6 and 1.7 109Chapter 2. Reliability and Risk 1112.1. Risk: notion and measurement 1112.1.1. Introductory notes 1112.1.2. Examples 1122.1.3. Risk notion 1142.1.4. Risk measurement 1152.1.5. Risk modeling 1182.1.6. Exercises 1202.2. Models of damage value 1202.2.1. Introductory remarks 1202.2.2. Simple damage models 1212.2.3. Compound damages. Methods of investigation 1252.2.4. Moments of compound damages 1302.2.5. Models of compound damages 1322.2.6. Examples 1362.2.7. Exercises 1372.3. Methods of risk analysis 1372.3.1. Introductory remarks 1372.3.2. Methodology of risk analysis 1382.3.3. Risk tree construction 1392.3.4. Risk tree rigging 1432.3.5. Risk tree analysis 1442.3.6. Exercise 1572.4. Bibliographical comments  1582.4.1. Section 2.1 1582.4.2. Section 2.2 1582.4.3. Section 2.3 158Chapter 3. Risk Management 1593.1. Insurance of risks and risk of insurance 1593.1.1. Introductory remarks 1593.1.2. Basic notions 1593.1.3. Risk insurance models 1613.1.4. Basic risk insurance problems 1623.1.5. Examples 1633.1.6. Exercises 1673.2. Some notions and methods of financial mathematics 1683.2.1. Principal notion of financial mathematics 1683.2.2. Simple interests 1703.2.3. Compound interests 1723.2.4. Cash flows and the financial rents 1743.2.5. Exercises 1773.3. Short-time insurance model investigation 1793.3.1. Introductory remarks 1793.3.2. Calculation of the individual claim indexes 1803.3.3. Exact calculation of summary claim characteristics 1823.3.4. Normal asymptotic of summary claim distribution 1833.3.5. Poisson asymptotic of summary claim distribution 1843.3.6. Calculation of insurance basic characteristics 1853.3.7. Exercises 1873.4. Long-time insurance model investigation 1883.4.1. Introductory remarks 1883.4.2. The basic parameters of long-time insurance contracts 1893.4.3. Insurance annuity analysis 1903.4.4. The net-premium calculation 1923.4.5. Insurance load calculation 1933.4.6. An example 1953.4.7. Exercises 1983.5. Bibliographical comments 1983.5.1. Section 3.1 1983.5.2. Section 3.2 1983.5.3. Sections 3.3 and 3.4 198Appendices 199Appendix 1 201Appendix 2 203Bibliography 207Index 209