This textbook provides the tools for a modern post-graduate introductory course on system reliability theory. It focuses on probabilistic aspects of the theory, including recent results based on signatures, stochastic orders, aging classes, copulas and distortion (or aggregation) functions. The reader requires on an introductory knowledge on probability theory and mathematics. The book serves both for graduate students in mathematics and for engineering students in various disciplines as well as students learning survival analysis, network reliability or simple game theory. Included also are brief introductions to the basic aspects of lifetime modelling, stochastic comparisons, aging classes, mixtures and copula theory. The book develops this knowledge with worked examples and supplies code for the program R so that students can explore its lessons and techniques.
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1 Coherent System Structures |
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1 | (22) |
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1 | (6) |
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7 | (8) |
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15 | (3) |
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15 | (1) |
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16 | (1) |
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17 | (1) |
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1.4 Multi-state Systems with Binary Components |
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18 | (5) |
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1.4.1 Binary Systems Associated to a Multi-state System |
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19 | (1) |
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1.4.2 Multi-state System Associated to a Binary System |
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20 | (3) |
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2 Coherent System Lifetimes |
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23 | (48) |
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2.1 Coherent System Lifetimes |
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23 | (1) |
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2.2 Reliability and Aging Functions |
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24 | (4) |
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2.3 Signature Representations |
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28 | (26) |
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2.4 Distortion Representations |
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54 | (17) |
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71 | (46) |
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3.1 Main Stochastic Orders |
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71 | (4) |
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3.2 Systems with IID or EXC Components |
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75 | (8) |
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3.3 Systems with ID Components |
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83 | (11) |
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3.4 Systems with Non-ID Components |
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94 | (15) |
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3.5 A Parrondo Paradox in Reliability |
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109 | (8) |
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117 | (30) |
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117 | (3) |
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4.2 Systems with ID Components |
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120 | (10) |
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4.3 Systems with Non-ID Components |
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130 | (3) |
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4.4 Residual and Inactivity Times of Systems |
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133 | (8) |
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141 | (3) |
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144 | (3) |
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5 Redundancy and Repair Properties |
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147 | (18) |
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147 | (6) |
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5.2 Systems with ID Components |
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153 | (2) |
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5.3 Systems with Non-ID Components |
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155 | (5) |
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160 | (5) |
| Glossary |
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165 | (2) |
| References |
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167 | (6) |
| Index |
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173 | |
Jorge Navarro is full professor in the Department of Statistics and Operational Research, located at the Faculty of Mathematics in the University of Murcia (Spain). He has more than one hundred research papers in this field. He appears in the Standford top researchers' list: 332/16942 in Stat. & Probab. Associate editor of IEEE Transactions on Reliability, since 2018 and Metrika, since 2017. Editor of Journal of Applied Probability, since 2016 and associate editor or board member of several other journals.
Lisainfo e-raamatute kohta