Reliability and Maintenance Modeling with Optimization: Advances and Applications

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Contributors
SECTION I: Stochastic Maintenance Policies
Chapter 1: Nine Memorial Research Works
1.1. Introduction
1.2. Two-unit Standby System
1.3. Imperfect PM (Preventive Maintenance)
1.4. Discrete Weibull Distribution
1.5. Definition of Minimal Repair
1.6. Shock and Damage Model
1.7. Finite Interval
1.8. Replacement First, Last, Overtime and Middle
1.9. Random K-out-of- n System
1.10. Asymptotic Calculations
Chapter 2: Replacement First and Last Policies with Random Times for Redundant Systems
2.1. Introduction
2.2. Random Age Replacement
2.2.1. Random Replacement Distribution
2.2.2. Replacement Policies for Single Unit System
2.3. Replacement Policies for Redundant System
2.4. Series System
2.5. Parallel System
2.6. Random K-out-of-n System
2.7. Numerical Examples of Four Redundant Systems with 4 Units
2.8. Conclusions
Chapter 3: Backup Policies with Random Data Updates
3.1. Introduction
3.2. Expected Cost Rates
3.3. Optimum Backup Times
3.3.1. Incremental Backup
3.3.1.1. Case I
3.3.1.2. Case II
3.3.2. Differential Backup
3.3.2.1. Case I
3.3.2.2. Case II
3.3.3. Numerical Example
3.4. Overtime Backup Models
3.5. Optimum Backup Times
3.5.1. Incremental Backup
3.5.1.1. Case I
3.5.1.2. Case II
3.5.2. Differential Backup
3.5.2.1. Case I
3.5.2.2. Case II
3.6. Comparisons of Update N and Overtime T
3.6.1. Incremental Backup
3.6.2. Differential Backup
3.6.3. Numerical Examples
3.7. Conclusions
Chapter 4: Main and Auxiliary Subsystem
4.1. Introduction
4.2. Assumptions and Modelling
4.3. Optimal Solution and Discussions
4.4. Extended Model for Systems with Dependent Parts
4.5. Numerical Examples
4.5.1. System with Independent Parts
4.5.2. System with Dependent Parts
4.6. Conclusion
Chapter 5: Extended Replacement Policy in Damage Models
5.1. Introduction
5.2. Description of General Replacement Policy
5.3. Formulation
5.4. Optimal Policy
5.5. Numerical Example
5.6. Conclusions
SECTION II: Reliability Modeling & Application
Chapter 6: Optimal Checking Policy for a Server System with a Cyber Attack
6.1. Introduction
6.2. Model 1
6.3. Model 2
6.4. Model 3
6.5. Model 4
6.6. Model 5
6.7. Numerical Examples
6.8. Conclusions
Chapter 7: Reliability Analysis of Congestion Control Scheme
7.1. Introduction
7.2. Congestion Control Scheme with FEC
7.2.1. Reliability Quantities
7.2.2. Optimal Policy
7.2.3. Example 1
7.3. Congestion Control Scheme with Hybrid ARQ
7.3.1. Reliability Quantities
7.3.2. Optimal Policy
7.3.3. Example 2
7.4. Conclusions
SECTION III: Warranty Analysis Manufacturing
Chapter 8: The Optimal Design of Consecutive-k Systems
8.1. Introduction
8.2. Consecutive-k Systems
8.3. Reliabilities of Consecutive-k Systems
8.3.1. System Reliability
8.3.2. Approximation Methods for System Reliability
8.4. Component Assignment Problem (CAP)
8.4.1. Efficient Algorithm for Obtaining the Optimal Arrangement
8.4.2. Algorithms for Obtaining Pseudo-Optimal Arrangement
8.5. Maintenance Problems
8.5.1. Maintenance Problems in Linear Consecutive-k-out-of-n:F System
8.5.2. Maintenance Problems in Linear Consecutive-k-out-of-n:G Systems
8.6. Conclusions
Chapter 9: Infrastructure Maintenance
9.1. Introduction
9.2. Basic Models
9.2.1. Model 1
9.2.2. Model 2
9.3. Model 3
9.4. Model 4
9.5. Extended Models
9.5.1. Model 5
9.5.2. Model 6
9.5.3. Model 7
9.5.4. Model 8
9.6. Conclusion
SECTION IV: Software Reliability and Testing
Chapter 10: Optimal Maintenance Problem with OSS-Oriented EVM for OSS Project
10.1. Introduction
10.2. Related Research
10.3. Effort Estimation Model Based on Stochastic Differential Equation
10.4. Assessment Measures for OSS-Oriented EVM
10.4.1. How to Use the OSS Project Data
10.4.2. How to Derive OSS-Oriented EVM Value
10.5. Optimum Maintenance Time Based on Wiener Process Models
10.6. Application of Proposed Method to Actual Data
10.6.1. Used Data Set
10.6.2. Numerical Examples for Optimum Maintenance Time
10.7. Conclusion
Chapter 11: Reliability Assessment Model Based on Wiener Process
11.1. Introduction
11.2. Wiener Process Modeling Based on Periodic Weight Functions
11.3. Parameter Estimation
11.4. Numerical Examples
11.5. Concluding Remarks
Chapter 12: Approximated Estimation of Software Target Failure Measures
12.1. Introduction
12.2. SIL and Target Failure Measures
12.3. Software Hazard Rate Modeling
12.4. Formulations of Target Failure Measures
12.5. Numerical Examples
12.6. Concluding Remarks
SECTION V: Maintenance Optimization and Applications
Chapter 13: PH Expansion of MRGP and Its Application to Reliability Problems
13.1. Introduction
13.2. Markov Regenerative Process
13.2.1. Structured MRGP
13.2.2. Stationary Analysis for Structured MRGP
13.3. PH Expansion of MRGP
13.3.1. PH Approximation
13.3.2. PH Expansion
13.4. Illustrative Examples
13.4.1. MRSPN to MRGP
13.4.2. PH Expansion
13.5. Conclusions
Chapter 14: A Hybrid Model Fitting Framework Considering Accuracy and Performance
14.1. Introduction
14.2. Software Reliability Growth Models
14.2.1. Nonhomogeneous Poisson Process Software Reliability Growth Models
14.2.2. Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models
14.3. Parameter Estimation Algorithms
14.3.1. Initial Parameter Estimates
14.3.2. Particle Swarm Optimization (PSO)
14.3.3. Expectation Conditional Maximization (ECM) Algorithm
14.3.4. Newton's Method (NM)
14.4. Illustrations
14.4.1. Nonhomogeneous Poisson Process Software Reliability Growth Models
14.4.1.1. PSO Tradeoff Analysis
14.4.1.2. Performance assessment
14.4.2. Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models
14.4.2.1. Constant and Variable Average Number of Function Evaluations
14.4.2.2. Performance Assessment
14.5. Conclusion and Future Work
Chapter 15: Alternating α-Series Process
15.1. Introduction
15.2. α-Series Process
15.3. Alternating α-Series Process
15.3.1. Introduction
15.3.2. Counting Process 1: N(t) Number of Cycles Completed by Time t
15.3.3. Counting Process 2: M(t) Number of Failures up to Time t
15.4. Mean and Variance of the Counting Processes N(t) and M(t)
15.4.1. Computing E(N(t)) and Var(N(t))
15.4.2. Computing E(M(t)) and Var(M(t))
15.5. Numerical Results
15.6. Application of an AAS Process to Modelling Warranty Data
15.6.1. Procedure for Fitting an AAS Process
15.6.2. Warranty Data
15.6.3. Fitting an AAS Process to the Warranty Claims Data
15.7. Conclusion
Chapter 16: Staggered Testing Strategy
16.1. Introduction
16.2. PFD of Redundant Safety Instrumented Systems with 2 and 3 Units
16.2.1. Optimal Staggered Testing in SIS with 1 out of 2 Structures
16.2.2. Optimal Staggered Testing in SIS with 1 out of 3 Structures (Equal Testing Interval)
16.3. Staggered Testing Strategies with Different Testing Intervals
16.3.1. Cases with Three Groups and Two Different Testing Intervals
16.3.2. Cases with Three Different Testing Intervals
16.3.3. Comparison between Different Testing Strategies
16.4. Cost Models of Staggered Testing Strategies
16.5. Conclusions
Chapter 17: Modules of Multi-State Systems
17.1. Introduction
17.2. Ordered Set Theoretical Preliminaries
17.2.1. Composite Function
17.2.2. Product Ordered Set
17.3. Basic Concepts
17.4. A Module of a System
17.4.1. Definition and Basic Properties
17.5. Hierarchy of Multi-State Systems
17.5.1. Homogeneous System
17.5.2. Three Modules Theorem of Binary-State Systems
17.6. EEBW system
17.7. Introduction to Three Modules Theorem for Multistate Systems
17.8. Concluding Remarks
Chapter 18: A Postponed Repair Model for a Mission-Based System
18.1. Introduction
18.2. Notations and Assumptions
18.3. Cost Model under the Proposed Policy
18.3.1. Expected Number of Missions Successively Completed by t
18.3.2. Three Renewal Cases and the Corresponding Occurrence Probabilities
18.3.2.1. A Failure Renewal
18.3.2.2. A Random Inspection Renewal
18.3.2.3. A Periodic Inspection Renewal
18.3.3. The Expected Renewal Cycle Cost
18.3.4. The Expected Renewal Cycle Length
18.4. Three Maintenance Policies
18.5. Numerical Examples
18.6. Conclusions and Further Research