Reliability and Maintenance Modeling with Optimization

Reliability and Maintenance Modeling with Optimization

by Mitsutaka Kimura, Satoshi Mizutani, Mitsuhiro Imaizumi, Kodo Ito
Released April 2023
Publisher(s): CRC Press
ISBN: 9781000849264

Read it now on the O’Reilly learning platform with a 10-day free trial.

O’Reilly members get unlimited access to books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial

Book description

Reliability and maintenance modeling with optimization is the most fundamental and interdisciplinary research area that can be applied to every technical and management field. Reliability and Maintenance Modeling with Optimization: Advances and Applications aims at providing the most recent advances and achievements in reliability and maintenance.

The book discusses replacement, repair, and inspection, offers estimation and statistical tests, covers accelerated life testing, explores warranty analysis manufacturing, and includes service reliability.

The targeted readers are researchers interested in reliability and maintenance engineering. The book can serve as supplemental reading in professional seminars for engineers, designers, project managers, and graduate students.

Table of contents

  1. Cover Page
  2. Half-Title Page
  3. Series
  4. Title Page
  5. Copyright Page
  6. Contents
  7. Preface
  8. Contributors
  9. Section I Stochastic Maintenance Policies
    1. Chapter 1 Nine Memorial Research Works
      1. 1.1 Introduction
      2. 1.2 Two-unit Standby System
      3. 1.3 Imperfect PM (Preventive Maintenance)
      4. 1.4 Discrete Weibull Distribution
      5. 1.5 Definition of Minimal Repair
      6. 1.6 Shock and Damage Model
      7. 1.7 Finite Interval
      8. 1.8 Replacement First, Last, Overtime and Middle
      9. 1.9 Random K-out-of-\tmspace+.1667emn System
      10. 1.10 Asymptotic Calculations
    2. Chapter 2 Replacement First and Last Policies with Random Times for Redundant Systems
      1. 2.1 Introduction
      2. 2.2 Random Age Replacement
        1. 2.2.1 Random Replacement Distribution
        2. 2.2.2 Replacement Policies for Single Unit System
      3. 2.3 Replacement Policies for Redundant System
      4. 2.4 Series System
      5. 2.5 Parallel System
      6. 2.6 Random K-out-of-n System
      7. 2.7 Numerical Examples of Four Redundant Systems with 4 Units
      8. 2.8 Conclusions
    3. Chapter 3 Backup Policies with Random Data Updates
      1. 3.1 Introduction
      2. 3.2 Expected Cost Rates
      3. 3.3 Optimum Backup Times
        1. 3.3.1 Incremental Backup
          1. 3.3.1.1 Case I
          2. 3.3.1.2 Case II
        2. 3.3.2 Differential Backup
          1. 3.3.2.1 Case I
          2. 3.3.2.2 Case II
        3. 3.3.3 Numerical Example
      4. 3.4 Overtime Backup Models
      5. 3.5 Optimum Backup Times
        1. 3.5.1 Incremental Backup
          1. 3.5.1.1 Case I
          2. 3.5.1.2 Case II
        2. 3.5.2 Differential Backup
          1. 3.5.2.1 Case I
          2. 3.5.2.2 Case II
      6. 3.6 Comparisons of Update N and Overtime T
        1. 3.6.1 Incremental Backup
        2. 3.6.2 Differential Backup
        3. 3.6.3 Numerical Examples
      7. 3.7 Conclusions
    4. Chapter 4 Main and Auxiliary Subsystem
      1. 4.1 Introduction
      2. 4.2 Assumptions and Modelling
      3. 4.3 Optimal Solution and Discussions
      4. 4.4 Extended Model for Systems with Dependent Parts
      5. 4.5 Numerical Examples
        1. 4.5.1 System with Independent Parts
        2. 4.5.2 System with Dependent Parts
      6. 4.6 Conclusion
    5. Chapter 5 Extended Replacement Policy in Damage Models
      1. 5.1 Introduction
      2. 5.2 Description of General Replacement Policy
      3. 5.3 Formulation
      4. 5.4 Optimal Policy
      5. 5.5 Numerical Example
      6. 5.6 Conclusions
  10. Section II Reliability Modeling & Application
    1. Chapter 6 Optimal Checking Policy for a Server System with a Cyber Attack
      1. 6.1 Introduction
      2. 6.2 Model 1
      3. 6.3 Model 2
      4. 6.4 Model 3
      5. 6.5 Model 4
      6. 6.6 Model 5
      7. 6.7 Numerical Examples
      8. 6.8 Conclusions
    2. Chapter 7 Reliability Analysis of Congestion Control Scheme
      1. 7.1 Introduction
      2. 7.2 Congestion Control Scheme with FEC
        1. 7.2.1 Reliability Quantities
        2. 7.2.2 Optimal Policy
        3. 7.2.3 Example 1
      3. 7.3 Congestion Control Scheme with Hybrid ARQ
        1. 7.3.1 Reliability Quantities
        2. 7.3.2 Optimal Policy
        3. 7.3.3 Example 2
      4. 7.4 Conclusions
  11. Section III Warranty Analysis Manufacturing
    1. Chapter 8 The Optimal Design of Consecutive-k Systems
      1. 8.1 Introduction
      2. 8.2 Consecutive-k Systems
      3. 8.3 Reliabilities of Consecutive-k Systems
        1. 8.3.1 System Reliability
        2. 8.3.2 Approximation Methods for System Reliability
      4. 8.4 Component Assignment Problem (CAP)
        1. 8.4.1 Efficient Algorithm for Obtaining the Optimal Arrangement
        2. 8.4.2 Algorithms for Obtaining Pseudo-Optimal Arrangement
      5. 8.5 Maintenance Problems
        1. 8.5.1 Maintenance Problems in Linear Consecutive-k-out-of-n:F System
        2. 8.5.2 Maintenance Problems in Linear Consecutive-k-out-of-n:G Systems
      6. 8.6 Conclusions
    2. Chapter 9 Infrastructure Maintenance
      1. 9.1 Introduction
      2. 9.2 Basic Models
        1. 9.2.1 Model 1
        2. 9.2.2 Model 2
      3. 9.3 Model 3
      4. 9.4 Model 4
      5. 9.5 Extended Models
        1. 9.5.1 Model 5
        2. 9.5.2 Model 6
        3. 9.5.3 Model 7
        4. 9.5.4 Model 8
      6. 9.6 Conclusion
  12. Section IV Software Reliability and Testing
    1. Chapter 10 Optimal Maintenance Problem with OSS-Oriented EVM for OSS Project
      1. 10.1 Introduction
      2. 10.2 Related Research
      3. 10.3 Effort Estimation Model Based on Stochastic Differential Equation
      4. 10.4 Assessment Measures for OSS-Oriented EVM
        1. 10.4.1 How to Use the OSS Project Data
        2. 10.4.2 How to Derive OSS-Oriented EVM Value
      5. 10.5 Optimum Maintenance Time Based on Wiener Process Models
      6. 10.6 Application of Proposed Method to Actual Data
        1. 10.6.1 Used Data Set
        2. 10.6.2 Numerical Examples for Optimum Maintenance Time
      7. 10.7 Conclusion
    2. Chapter 11 Reliability Assessment Model Based on Wiener Process
      1. 11.1 Introduction
      2. 11.2 Wiener Process Modeling Based on Periodic Weight Functions
      3. 11.3 Parameter Estimation
      4. 11.4 Numerical Examples
      5. 11.5 Concluding Remarks
    3. Chapter 12 Approximated Estimation of Software Target Failure Measures
      1. 12.1 Introduction
      2. 12.2 SIL and Target Failure Measures
      3. 12.3 Software Hazard Rate Modeling
      4. 12.4 Formulations of Target Failure Measures
      5. 12.5 Numerical Examples
      6. 12.6 Concluding Remarks
  13. Section V Maintenance Optimization and Applications
    1. Chapter 13 PH Expansion of MRGP and Its Application to Reliability Problems
      1. 13.1 Introduction
      2. 13.2 Markov Regenerative Process
        1. 13.2.1 Structured MRGP
        2. 13.2.2 Stationary Analysis for Structured MRGP
      3. 13.3 PH Expansion of MRGP
        1. 13.3.1 PH Approximation
        2. 13.3.2 PH Expansion
      4. 13.4 Illustrative Examples
        1. 13.4.1 MRSPN to MRGP
        2. 13.4.2 PH Expansion
      5. 13.5 Conclusions
    2. Chapter 14 A Hybrid Model Fitting Framework Considering Accuracy and Performance
      1. 14.1 Introduction
      2. 14.2 Software Reliability Growth Models
        1. 14.2.1 Nonhomogeneous Poisson Process Software Reliability Growth Models
        2. 14.2.2 Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models
      3. 14.3 Parameter Estimation Algorithms
        1. 14.3.1 Initial Parameter Estimates
        2. 14.3.2 Particle Swarm Optimization (PSO)
        3. 14.3.3 Expectation Conditional Maximization (ECM) Algorithm
        4. 14.3.4 Newton's Method (NM)
      4. 14.4 Illustrations
        1. 14.4.1 Nonhomogeneous Poisson Process Software Reliability Growth Models
          1. 14.4.1.1 PSO Tradeoff Analysis
          2. 14.4.1.2 Performance assessment
        2. 14.4.2 Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models
          1. 14.4.2.1 Constant and Variable Average Number of Function Evaluations
          2. 14.4.2.2 Performance Assessment
      5. 14.5 Conclusion and Future Work
    3. Chapter 15 Alternating α-Series Process
      1. 15.1 Introduction
      2. 15.2 α-Series Process
      3. 15.3 Alternating α-Series Process
        1. 15.3.1 Introduction
        2. 15.3.2 Counting Process 1: N(t) Number of Cycles Completed by Time t
        3. 15.3.3 Counting Process 2: M(t) Number of Failures up to Time t
      4. 15.4 Mean and Variance of the Counting Processes N( t) and M( t)
        1. 15.4.1 Computing E(N( t)) and V ar( N( t))
        2. 15.4.2 Computing E(M( t)) and V ar( M( t))
      5. 15.5 Numerical Results
      6. 15.6 Application of an AAS Process to Modelling Warranty Data
        1. 15.6.1 Procedure for Fitting an AAS Process
        2. 15.6.2 Warranty Data
        3. 15.6.3 Fitting an AAS Process to the Warranty Claims Data
      7. 15.7 Conclusion
    4. Chapter 16 Staggered Testing Strategy
      1. 16.1 Introduction
      2. 16.2 PFD of Redundant Safety Instrumented Systems with 2 and 3 Units
        1. 16.2.1 Optimal Staggered Testing in SIS with 1 out of 2 Structures
        2. 16.2.2 Optimal Staggered Testing in SIS with 1 out of 3 Structures (Equal Testing Interval)
      3. 16.3 Staggered Testing Strategies with Different Testing Intervals
        1. 16.3.1 Cases with Three Groups and Two Different Testing Intervals
        2. 16.3.2 Cases with Three Different Testing Intervals
        3. 16.3.3 Comparison between Different Testing Strategies
      4. 16.4 Cost Models of Staggered Testing Strategies
      5. 16.5 Conclusions
    5. Chapter 17 Modules of Multi-State Systems
      1. 17.1 Introduction
      2. 17.2 Ordered Set Theoretical Preliminaries
        1. 17.2.1 Composite Function
        2. 17.2.2 Product Ordered Set
      3. 17.3 Basic Concepts
      4. 17.4 A Module of a System
        1. 17.4.1 Definition and Basic Properties
      5. 17.5 Hierarchy of Multi-State Systems
        1. 17.5.1 Homogeneous System
        2. 17.5.2 Three Modules Theorem of Binary-State Systems
      6. 17.6 EEBW system
      7. 17.7 Introduction to Three Modules Theorem for Multi-state Systems
      8. 17.8 Concluding Remarks
    6. Chapter 18 A Postponed Repair Model for a Mission-Based System
      1. 18.1 Introduction
      2. 18.2 Notations and Assumptions
      3. 18.3 Cost Model under the Proposed Policy
        1. 18.3.1 Expected Number of Missions Successively Completed by t
        2. 18.3.2 Three Renewal Cases and the Corresponding Occurrence Probabilities
          1. 18.3.2.1 A Failure Renewal
          2. 18.3.2.2 A Random Inspection Renewal
          3. 18.3.2.3 A Periodic Inspection Renewal
        3. 18.3.3 The Expected Renewal Cycle Cost
        4. 18.3.4 The Expected Renewal Cycle Length
      4. 18.4 Three Maintenance Policies
      5. 18.5 Numerical Examples
      6. 18.6 Conclusions and Further Research

Product information

  • Title: Reliability and Maintenance Modeling with Optimization
  • Author(s): Mitsutaka Kimura, Satoshi Mizutani, Mitsuhiro Imaizumi, Kodo Ito
  • Release date: April 2023
  • Publisher(s): CRC Press
  • ISBN: 9781000849264