Preface. Acknowledgments. 1 Introduction. 1.1 Needs for Reliability Modeling. 1.2 Optimal Design. 2 Reliability Mathematics.
2.1 Probability and Distributions. 2.1.1 Events and Boolean Algebra. 2.1.2 Probabilities of Events.
2.1.3 Random Variables and Their Characteristics. 2.1.4 Multivariate Distributions. 2.1.
5 Special Discrete Distributions. 2.1.6 Special Continuous Distributions. 2.2 Reliability Concepts. 2.3 Commonly Used Lifetime Distributions.
2.4 Stochastic Processes. 2.4.1 General Definitions. 2.4.2 Homogeneous Poisson Process.
2.4.3 Nonhomogeneous Poisson Process. 2.4.4 Renewal Process. 2.4.
5 Discrete-Time Markov Chains. 2.4.6 Continuous-Time Markov Chains. 2.5 Complex System Reliability Assessment Using Fault Tree Analysis. 3 Complexity Analysis. 3.
1 Orders of Magnitude and Growth. 3.2 Evaluation of Summations. 3.3 Bounding Summations. 3.4 Recurrence Relations. 3.
4.1 Expansion Method. 3.4.2 Guess-and-Prove Method. 3.4.3 Master Method.
3.5 Summary. 4 Fundamental System Reliability Models. 4.1 Reliability Block Diagram. 4.2 Structure Functions. 4.
3 Coherent Systems. 4.4 Minimal Paths and Minimal Cuts. 4.5 Logic Functions. 4.6 Modules within a Coherent System. 4.
7 Measures of Performance. 4.8 One-Component System. 4.9 Series System Model. 4.9.1 System Reliability Function and MTTF.
4.9.2 System Availability. 4.10 Parallel System Model. 4.10.1 System Reliability Function and MTTF.
4.10.2 System Availability of Parallel System with Two i.i.d. Components. 4.10.
3 System Availability of Parallel System with Two Different Components. 4.10.4 Parallel Systems with n i.i.d. Components. 4.
11 Parallel-Series System Model. 4.12 Series-Parallel System Model. 4.13 Standby System Model. 4.13.1 Cold Standby Systems.
4.13.2 Warm Standby Systems. 5 General Methods for System Reliability Evaluation. 5.1 Parallel and Series Reductions. 5.2 Pivotal Decomposition.
5.3 Generation of Minimal Paths and Minimal Cuts. 5.3.1 Connection Matrix. 5.3.2 Node Removal Method for Generation of Minimal Paths.
5.3.3 Generation of Minimal Cuts from Minimal Paths. 5.4 Inclusion-Exclusion Method. 5.5 Sum-of-Disjoint-Products Method. 5.
6 Markov Chain Imbeddable Structures. 5.6.1 MIS Technique in Terms of System Failures. 5.6.2 MIS Technique in Terms of System Success. 5.
7 Delta-Star and Star-Delta Transformations. 5.7.1 Star or Delta Structure with One Input Node and Two Output Nodes. 5.7.2 Delta Structure in Which Each Node May Be either an Input Node or an Output Node. 5.
8 Bounds on System Reliability. 5.8.1 IE Method. 5.8.2 SDP Method. 5.
8.3 Esary-Proschan (EP) Method. 5.8.4 Min-Max Bounds. 5.8.5 Modular Decompositions.
5.8.6 Notes. 6 General Methodology for System Design. 6.1 Redundancy in System Design. 6.2 Measures of Component Importance.
6.2.1 Structural Importance. 6.2.2 Reliability Importance. 6.2.
3 Criticality Importance. 6.2.4 Relative Criticality. 6.3 Majorization and Its Application in Reliability. 6.3.
1 Definition of Majorization. 6.3.2 Schur Functions. 6.3.3 L-Additive Functions. 6.
4 Reliability Importance in Optimal Design. 6.5 Pairwise Rearrangement in Optimal Design. 6.6 Optimal Arrangement for Series and Parallel Systems. 6.7 Optimal Arrangement for Series-Parallel Systems. 6.
8 Optimal Arrangement for Parallel-Series Systems. 6.9 Two-Stage Systems. 6.10 Summary. 7 Thek-out-of-n System Model. 7.1 System Reliability Evaluation.
7.1.1 The k-out-of-n:G System with i.i.d. Components. 7.1.
2 The k-out-of-n:G System with Independent Components. 7.1.3 Bounds on System Reliability. 7.2 Relationship between k-out-of-n G and F Systems. 7.2.
1 Equivalence betwe.