book

Reliability and Maintenance Modeling with Optimization

Name: Reliability and Maintenance Modeling with Optimization
ISBN: 9781000849264

by Mitsutaka Kimura, Satoshi Mizutani, Mitsuhiro Imaizumi, Kodo Ito

April 2023

Intermediate to advanced

372 pages

8h 15m

English

CRC Press

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Cover Page
Half-Title Page
Series
Title Page
Copyright Page
Contents
Preface
Contributors
Section I Stochastic Maintenance Policies
Chapter 1 Nine Memorial Research Works
1.1 Introduction1.2 Two-unit Standby System1.3 Imperfect PM (Preventive Maintenance)1.4 Discrete Weibull Distribution1.5 Definition of Minimal Repair1.6 Shock and Damage Model1.7 Finite Interval1.8 Replacement First, Last, Overtime and Middle1.9 Random K-out-of-\tmspace+.1667emn System1.10 Asymptotic Calculations

Chapter 2 Replacement First and Last Policies with Random Times for Redundant Systems
2.1 Introduction2.2 Random Age Replacement2.2.1 Random Replacement Distribution2.2.2 Replacement Policies for Single Unit System2.3 Replacement Policies for Redundant System2.4 Series System2.5 Parallel System2.6 Random K-out-of-n System2.7 Numerical Examples of Four Redundant Systems with 4 Units2.8 Conclusions
Chapter 3 Backup Policies with Random Data Updates
3.1 Introduction3.2 Expected Cost Rates3.3 Optimum Backup Times3.3.1 Incremental Backup3.3.1.1 Case I3.3.1.2 Case II3.3.2 Differential Backup3.3.2.1 Case I3.3.2.2 Case II3.3.3 Numerical Example3.4 Overtime Backup Models3.5 Optimum Backup Times3.5.1 Incremental Backup3.5.1.1 Case I3.5.1.2 Case II3.5.2 Differential Backup3.5.2.1 Case I3.5.2.2 Case II3.6 Comparisons of Update N and Overtime T3.6.1 Incremental Backup3.6.2 Differential Backup3.6.3 Numerical Examples3.7 Conclusions
Chapter 4 Main and Auxiliary Subsystem
4.1 Introduction4.2 Assumptions and Modelling4.3 Optimal Solution and Discussions4.4 Extended Model for Systems with Dependent Parts4.5 Numerical Examples4.5.1 System with Independent Parts4.5.2 System with Dependent Parts4.6 Conclusion
Chapter 5 Extended Replacement Policy in Damage Models
5.1 Introduction5.2 Description of General Replacement Policy5.3 Formulation5.4 Optimal Policy5.5 Numerical Example5.6 Conclusions
Section II Reliability Modeling & Application
Chapter 6 Optimal Checking Policy for a Server System with a Cyber Attack
6.1 Introduction6.2 Model 16.3 Model 26.4 Model 36.5 Model 46.6 Model 56.7 Numerical Examples6.8 Conclusions
Chapter 7 Reliability Analysis of Congestion Control Scheme
7.1 Introduction7.2 Congestion Control Scheme with FEC7.2.1 Reliability Quantities7.2.2 Optimal Policy7.2.3 Example 17.3 Congestion Control Scheme with Hybrid ARQ7.3.1 Reliability Quantities7.3.2 Optimal Policy7.3.3 Example 27.4 Conclusions
Section III Warranty Analysis Manufacturing
Chapter 8 The Optimal Design of Consecutive-k Systems
8.1 Introduction8.2 Consecutive-k Systems8.3 Reliabilities of Consecutive-k Systems8.3.1 System Reliability8.3.2 Approximation Methods for System Reliability8.4 Component Assignment Problem (CAP)8.4.1 Efficient Algorithm for Obtaining the Optimal Arrangement8.4.2 Algorithms for Obtaining Pseudo-Optimal Arrangement8.5 Maintenance Problems8.5.1 Maintenance Problems in Linear Consecutive-k-out-of-n:F System8.5.2 Maintenance Problems in Linear Consecutive-k-out-of-n:G Systems8.6 Conclusions
Chapter 9 Infrastructure Maintenance
9.1 Introduction9.2 Basic Models9.2.1 Model 19.2.2 Model 29.3 Model 39.4 Model 49.5 Extended Models9.5.1 Model 59.5.2 Model 69.5.3 Model 79.5.4 Model 89.6 Conclusion
Section IV Software Reliability and Testing
Chapter 10 Optimal Maintenance Problem with OSS-Oriented EVM for OSS Project
10.1 Introduction10.2 Related Research10.3 Effort Estimation Model Based on Stochastic Differential Equation10.4 Assessment Measures for OSS-Oriented EVM10.4.1 How to Use the OSS Project Data10.4.2 How to Derive OSS-Oriented EVM Value10.5 Optimum Maintenance Time Based on Wiener Process Models10.6 Application of Proposed Method to Actual Data10.6.1 Used Data Set10.6.2 Numerical Examples for Optimum Maintenance Time10.7 Conclusion
Chapter 11 Reliability Assessment Model Based on Wiener Process
11.1 Introduction11.2 Wiener Process Modeling Based on Periodic Weight Functions11.3 Parameter Estimation11.4 Numerical Examples11.5 Concluding Remarks
Chapter 12 Approximated Estimation of Software Target Failure Measures
12.1 Introduction12.2 SIL and Target Failure Measures12.3 Software Hazard Rate Modeling12.4 Formulations of Target Failure Measures12.5 Numerical Examples12.6 Concluding Remarks
Section V Maintenance Optimization and Applications
Chapter 13 PH Expansion of MRGP and Its Application to Reliability Problems
13.1 Introduction13.2 Markov Regenerative Process13.2.1 Structured MRGP13.2.2 Stationary Analysis for Structured MRGP13.3 PH Expansion of MRGP13.3.1 PH Approximation13.3.2 PH Expansion13.4 Illustrative Examples13.4.1 MRSPN to MRGP13.4.2 PH Expansion13.5 Conclusions
Chapter 14 A Hybrid Model Fitting Framework Considering Accuracy and Performance
14.1 Introduction14.2 Software Reliability Growth Models14.2.1 Nonhomogeneous Poisson Process Software Reliability Growth Models14.2.2 Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models14.3 Parameter Estimation Algorithms14.3.1 Initial Parameter Estimates14.3.2 Particle Swarm Optimization (PSO)14.3.3 Expectation Conditional Maximization (ECM) Algorithm14.3.4 Newton's Method (NM)14.4 Illustrations14.4.1 Nonhomogeneous Poisson Process Software Reliability Growth Models14.4.1.1 PSO Tradeoff Analysis14.4.1.2 Performance assessment14.4.2 Discrete Cox Proportional Hazard NHPP Software Reliability Growth Models14.4.2.1 Constant and Variable Average Number of Function Evaluations14.4.2.2 Performance Assessment14.5 Conclusion and Future Work
Chapter 15 Alternating α-Series Process
15.1 Introduction15.2 α-Series Process15.3 Alternating α-Series Process15.3.1 Introduction15.3.2 Counting Process 1: N(t) Number of Cycles Completed by Time t15.3.3 Counting Process 2: M(t) Number of Failures up to Time t15.4 Mean and Variance of the Counting Processes N( t) and M( t)15.4.1 Computing E(N( t)) and V ar( N( t))15.4.2 Computing E(M( t)) and V ar( M( t))15.5 Numerical Results15.6 Application of an AAS Process to Modelling Warranty Data15.6.1 Procedure for Fitting an AAS Process15.6.2 Warranty Data15.6.3 Fitting an AAS Process to the Warranty Claims Data15.7 Conclusion
Chapter 16 Staggered Testing Strategy
16.1 Introduction16.2 PFD of Redundant Safety Instrumented Systems with 2 and 3 Units16.2.1 Optimal Staggered Testing in SIS with 1 out of 2 Structures16.2.2 Optimal Staggered Testing in SIS with 1 out of 3 Structures (Equal Testing Interval)16.3 Staggered Testing Strategies with Different Testing Intervals16.3.1 Cases with Three Groups and Two Different Testing Intervals16.3.2 Cases with Three Different Testing Intervals16.3.3 Comparison between Different Testing Strategies16.4 Cost Models of Staggered Testing Strategies16.5 Conclusions
Chapter 17 Modules of Multi-State Systems
17.1 Introduction17.2 Ordered Set Theoretical Preliminaries17.2.1 Composite Function17.2.2 Product Ordered Set17.3 Basic Concepts17.4 A Module of a System17.4.1 Definition and Basic Properties17.5 Hierarchy of Multi-State Systems17.5.1 Homogeneous System17.5.2 Three Modules Theorem of Binary-State Systems17.6 EEBW system17.7 Introduction to Three Modules Theorem for Multi-state Systems17.8 Concluding Remarks
Chapter 18 A Postponed Repair Model for a Mission-Based System
18.1 Introduction18.2 Notations and Assumptions18.3 Cost Model under the Proposed Policy18.3.1 Expected Number of Missions Successively Completed by t18.3.2 Three Renewal Cases and the Corresponding Occurrence Probabilities18.3.2.1 A Failure Renewal18.3.2.2 A Random Inspection Renewal18.3.2.3 A Periodic Inspection Renewal18.3.3 The Expected Renewal Cycle Cost18.3.4 The Expected Renewal Cycle Length18.4 Three Maintenance Policies18.5 Numerical Examples18.6 Conclusions and Further Research

Overview

Reliability and maintenance modeling with optimization is the most fundamental and interdisciplinary research area and it can be applied to every technical and management field. This monograph provides the most recent advances and achievements in reliability and maintenance.

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