Handbook of Reliability Engineering

PART I. System Reliability and Optimization1 Multi-state k-out-of-n SystemsMing J. Zuo, Jinsheng Huang and Way Kuo1.1 Introduction1.2 Relevant Concepts in Binary Reliability Theory1.3 Binary k-out-of-n Models1.3.1 The k-out-of-n:G System with Independently and Identically Distributed Components1.3.2 Reliability Evaluation Using Minimal Path or Cut Sets1.3.3 Recursive Algorithms1.3.4 Equivalence Between a k-out-of-n:G System and an (n - k + 1)-out-of-n:F System1.3.5 The Dual Relationship Between the k-out-of-n G and F Systems1.4 Relevant Concepts in Multi-state Reliability Theory1.5 A Simple Multi-state k-out-of-n: G Model1.6 A Generalized Multi-state k-out-of-n:G System Model1.7 Properties of Generalized Multi-state k-out-of-n:G Systems1.8 Equivalence and Duality in Generalized Multi-state k-out-of-n Systems2 Reliability of Systems with Multiple Failure ModesHoang Pham2.1 Introduction2.2 The Series System2.3 The Parallel System2.3.1 Cost Optimization2.4 The Parallel-Series System2.4.1 The Profit Maximization Problem2.4.2 Optimization Problem2.5 The Series-Parallel System2.5.1 Maximizing the Average System Profit2.5.2 Consideration of Type I Design Error2.6 The k-out-of-n Systems2.6.1 Minimizing the Average System Cost2.7 Fault-tolerant Systems2.7.1 Reliability Evaluation2.7.2 Redundancy Optimization2.8 Weighted Systems with Three Failure Modes3 Reliabilities of Consecutive-k SystemsJen-Chun Chang and Frank K. Hwang3.1 Introduction3.1.1 Background3.1.2 Notation3.2 Computation of Reliability3.2.1 The Recursive Equation Approach3.2.2 The Markov Chain Approach3.2.3 Asymptotic Analysis3.3 Invariant Consecutive Systems3.3.1 Invariant Consecutive-2Systems3.3.2 Invariant Consecutive-k Systems3.3.3 Invariant Consecutive-kG System.3.4 Component Importance and the Component Replacement Problem3.4.1 The Birnbaum Importance3.4.2 Partial Birnbaum Importance3.4.3 The Optimal Component Replacement3.5 The Weighted-consecutive-k-out-of-n System.3.5.1 The Linear

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