Abdelkhalak El Hami is a university professor at INSA Rouen Normandie, France. He specializes in optimization, reliability and AI of multi-physical systems.Mohamed Eid is an associate professor at INSA Rouen Normandie, France. He is an expert in complex, multidisciplinary and multisectoral system performance modeling.

• Introduction ixChapter 1 Basic Notions 11.1 Introduction 11.2 Logical notions 21.2.1 Axioms 31.2.2 Elementary laws 51.3 Probabilistic notions 51.3.1 Probability D(t) and probability density ρ(t) 51.3.2 Failure occurrence rate λ(t) 61.3.3 Independent random events 71.4 System functional description 81.5 Binary system and basic model 101.6 The availability of binary systems 111.7 The sojourn probabilities 151.7.1 Reliability model 151.7.2 Maintainability 171.8 Failure, repair and stochastic processes 191.8.1 Renewable stochastic processes 201.8.2 Conditionally renewable stochastic processes 221.9 Multistate system 24Chapter 2 Modeling of Multistate Systems 272.1 Systems with analytical representation 282.2 Critical transitions 322.3 Binarization of multistate systems 322.4 Failure-to-start probability 372.5 Forbidden transitions 372.6 Boolean models and state graphs equivalence 392.7 Systems with systemic structure representation 412.8 The Markov graph 43Chapter 3 Matrix-like System 473.1 Introduction 473.2 Modeling the functional state of the system 483.2.1 Modeling a line of elementary components 493.2.2 System functional space modeling 493.2.3 The subspaces of sets 563.2.4 Transitions between sets 573.2.5 Modeling of equivalent rates of transitions 583.2.6 Dynamic modeling of operating states 613.3 Homogeneous matrix-like system 623.4 Academic case 643.4.1 Case specifications 643.4.2 Determine system performance 653.4.3 Results 653.5 Conclusion 65Chapter 4 Modeling of Systems with Redundancy 694.1 Introduction 694.2 Combinatorial analysis of the n/N system 704.3 Determining the availability/unavailability 714.3.1 Analysis by the binary structure function 714.3.2 Analysis by Boolean expressions 724.3.3 Example of analysis using Boolean expressions 754.4 The equivalent failure and repair rates 774.5 Homogeneous system 794.5.1 Characterization of the homogeneous system 794.6 Numerical application (1) 804.7 Numerical application (2) 824.7.1 Mission success criteria and system data 824.7.2 Functional modeling by state graph 824.7.3 System availability modeling 834.7.4 Modeling system unavailability 854.7.5 Modeling the equivalent failure rate of the system 864.7.6 The mean time before detection 874.7.7 Redundancy effectiveness assessment 88Chapter 5 System Reliability -- Application 915.1 Description of the system 925.2 System missions 935.3 Basic data 935.4 System unavailability modeling 945.5 System unavailability assessment 965.6 System availability modeling 985.7 System availability assessment 995.8 Reliability modeling 1005.9 System reliability assessment 1045.10 Analysis of the relative importance of components 1055.10.1 The predictive importance index 1055.10.2 The operational importance index 1075.11 Conclusion 111Chapter 6 Sequential Events -- Modeling and Analysis 1136.1 Introduction 1136.2 Sequential analysis with variable time intervals 1166.3 Sequential analysis with fixed time intervals 1226.4 Conclusion 124Chapter 7 The Monte Carlo Simulation Method 1257.1 Generation of random variables 1257.2 Sampling 1277.3 Analytical bijective sampling 1277.4 Generic Monte Carlo simulation approach 1307.5 Simulation of transitions in a multistate system 1327.5.1 The transition simulation approach 1347.5.2 Transitions simulation algorithm 1357.5.3 Transition histogram simulation results 1367.5.4 The number of sojourns by state 1397.5.5 Sojourn time by state 1407.5.6 The failure probability 1417.6 Simulation of the operation of a redundant system 1437.6.1 System description 1447.6.2 Operation histogram generation algorithm 1447.6.3 Operation histogram 1467.6.4 The mean time to fail 1477.6.5 Algorithm for determining system reliability 1497.6.6 System reliability estimation 1507.7 Conclusion 151Chapter 8 Physical Tests used in Reliability 1538.1 Introduction 1538.2 Accelerated tests 1558.2.1 The different acceleration laws 1568.3 Simple mechanical fatigue, Wöhler model 1598.3.1 Empirical laws of fatigue 1618.4 Aggravated tests 1628.4.1 The main aggravated tests 1638.5 Bayesian tests 1728.6 Fatigue damage analysis 1738.6.1 Formulations and development 1738.6.2 Fatigue damage 1768.7 Methodology of improvement using physical tests 1788.7.1 Optimization of the physical tests to be carried out 1788.8 Conclusion 182Appendix: Common Reliability Modeling Laws 185References 191Index 195