Comprehensive coverage of system reliability evaluation and optimal systems design

Optimal Reliability Modeling presents a complete volume of information and strategies for determining the most effective ways to make systems meet all necessary performance requirements, while considering schedule, cost, and feasibility. This practical book interprets, evaluates, and provides examples of all reliability systems in both binary and multistate contexts, including parallel, series, standby, k-out-of-n and consecutive-k-out-of-n, and general system models, as well as providing detailed explanations of system design to better diagnose, maintain, and improve existing systems.

Vital topics that make Optimal Reliability Modeling a powerful hands-on tool include:

• Complexity analysis-for background knowledge on efficiency comparisons of system reliability evaluation algorithms
• The Markov chain imbeddable structure-an effective tool for system reliability analysis
• Majorization-a powerful tool for the development of invariant optimal designs for some system structures
• The multistate system reliability theory-systematically introduced for the first time in a text on engineering system reliability analysis
• The latest k-out-of-n and consecutive-k-out-of-n system models-includes physical explanations and various applications

Optimal Reliability Modeling is the ideal book on system reliability for statisticians; industrial, electrical, computer, and mechanical engineers; and researchers and students.

Contents

1 Introduction.

• 1.1 Needs for Reliability Modeling.
• 1.2 Optimal Design.

2 Reliability Mathematics.

• 2.1 Probability and Distributions.
• 2.2 Reliability Concepts.
• 2.3 Commonly Used Lifetime Distributions.
• 2.4 Stochastic Processes.
• 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.
• 3.5 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.
• 4.10 Parallel System Model.
• 4.11 Parallel Series System Model.
• 4.12 Series Parallel System Model.
• 4.13 Standby System Model.

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.
• 5.4 Inclusion Exclusion Method.
• 5.5 Sum-of-Disjoint-Products Method.
• 5.6 Markov Chain Imbeddable Structures.
• 5.7 Delta Star and Star Delta Transformations.
• 5.8 Bounds on System Reliability.

6 General Methodology for System Design.

• 6.1 Redundancy in System Design.
• 6.2 Measures of Component Importance.
• 6.3 Majorization and Its Application in Reliability.
• 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.
• 7.2 Relationship between k-out-of-n G and F Systems.
• 7.3 Nonrepairable k-out-of-n Systems.
• 7.4 Repairable k-out-of-n Systems.
• 7.5 Weighted k-out-of-n:G Systems.

8 Design of k-out-of-n Systems.

• 8.1 Properties of k-out-of-n Systems.
• 8.2 Optimal Design of k-out-of-n Systems.
• 8.3 Fault Coverage.
• 8.4 Common-Cause Failures.
• 8.5 Dual Failure Modes.
• 8.6 Other Issues.

9 Consecutive-k-out-of-n Systems.

• 9.2 Optimal System Design.
• 9.3 Consecutive-k-out-of-n:G Systems.
• 9.4 System Lifetime Distribution.
• 9.5 Summary.

10 Multidimensional Consecutive-k-out-of-n Systems.

• 10.1 System Reliability Evaluation.
• 10.2 System Logic Functions.
• 10.3 Optimal System Design.
• 10.4 Summary.

11 Other k-out-of-n and Consecutive-k-out-of-n Models.

• 11.1 The s-Stage k-out-of-n Systems.
• 11.2 Redundant Consecutive-k-out-of-n Systems.
• 11.3 Linear and Circular m-Consecutive-k-out-of-n Model.
• 11.4 The k-within-Consecutive-m-out-of-n Systems.
• 11.5 Series Consecutive-k-out-of-n Systems.
• 11.6 Combined k-out-of-n:F and Consecutive-kc-out-of-n:F System.
• 11.7 Combined k-out-of-mn:F and Linear (r, s)/(m, n):F System.
• 11.8 Combined k-out-of-mn:F, One-Dimensional Con/kc/n:F, and Two-Dimensional Linear (r, s)/(m, n):F Model.
• 11.9 Application of Combined k-out-of-n and Consecutive-k-out-of-n Systems.
• 11.10 Consecutively Connected Systems.
• 11.11 Weighted Consecutive-k-out-of-n Systems.

12 Multistate System Models.

• 12.1 Consecutively Connected Systems with Binary System State and Multistate Components.
• 12.2 Two-Way Consecutively Connected Systems.
• 12.3 Key Concepts in Multistate Reliability Theory.
• 12.4 Special Multistate Systems and Their Performance Evaluation.
• 12.5 General Multistate Systems and Their Performance Evaluation.
• 12.6 Summary.