This is the first book on the Which-Is-Better (WIB) Problem. These are questions that in daily life include such as “Which is larger, younger and stronger?".
The main objective of this book is summarizing WIB Problems in maintenance and reliability theory. Optimal policies of replacement first, last and overtime are derived and compared theoretically and numerically, and WIB policies are determined. Furthermore, the reliability properties of parallel and standby systems are compared, and WIB system is determined. These WIB Problems are applied to shock and damage models and backup and checkpoint models of computer systems.
Author(s): Satoshi Mizutani, Xufeng Zhao, Toshio Nakagawa
Series: Springer Series in Reliability Engineering
Publisher: Springer
Year: 2023
Language: English
Pages: 280
City: Cham
Preface
Contents
1 Introduction
1.1 Maintenance Policies
1.2 Reliability Applications
References
2 Random Age Replacement Model
2.1 Random Replacement
2.2 Replacement First
2.3 Replacement Last
2.4 Replacement First and Last
2.5 Replacement Overtime
2.5.1 Replacement Overtime First
2.5.2 Replacement Overtime Last
2.6 Deviation Time
2.7 Problems
References
3 Replacement Model with Minimal Repair
3.1 Random Replacement
3.2 Replacement with Working Number
3.2.1 Replacement First
3.2.2 Replacement Last
3.3 Replacement First and Last
3.4 Replacement with Failure Number
3.4.1 Replacement First
3.4.2 Replacement Last
3.5 Replacement Overtime with Working Number
3.5.1 Replacement First
3.5.2 Replacement Last
3.6 Replacement Overtime with Failure Number
3.6.1 Replacement First
3.6.2 Replacement Last
3.7 Replacement with Working and Failure Numbers
3.7.1 Replacement First
3.7.2 Replacement Last
3.8 Problems
References
4 Periodic Replacement Models
4.1 Age Replacement
4.1.1 Replacement First
4.1.2 Replacement Last
4.2 Replacement with Working Number
4.2.1 Replacement First
4.2.2 Replacement Last
4.3 Replacement with Failure Number
4.3.1 Replacement First
4.3.2 Replacement Last
4.4 Replacement Over Failure Number
4.4.1 Replacement First
4.4.2 Replacement Last
4.5 Problems
References
5 Extended Replacement Models
5.1 Replacement with Two Failure Modes
5.1.1 Replacement First
5.1.2 Replacement Last
5.2 Undertime Replacement Model
5.2.1 Age Replacement
5.2.2 Replacement with Minimal Repair
5.3 Middle Replacement Models
5.3.1 Age Replacement
5.3.2 Comparison of Three Policies
5.3.3 Replacement with Minimal Repair
5.3.4 Comparisons of Three Policies
5.4 Problems
References
6 Which is Better for Standby or Parallel Systems
6.1 Reliability Measures
6.1.1 Constant Number of Units
6.1.2 Random Number of Units
6.2 Replacement Policies
6.2.1 MTTF for Replacement Time
6.2.2 Replacement for Number of Units
6.3 Scheduling of Random Works
6.3.1 Tandem and Parallel Works
6.3.2 Standby and Parallel Systems
6.3.3 Random Tandem Works
6.4 Modified Models
6.5 Problems
References
7 Which is Better Problems in Shock and Damage Models
7.1 Three Replacement Policies
7.2 Optimal Policies with Two Variables
7.3 Exponential Shock Times and Amount of Damage
7.4 Replacement Overtime Policies
7.5 Modified Replacement Models
References
8 Which is Better Problems in Backup Models
8.1 Database Backup Models
8.1.1 Optimal Backup Times
8.2 Overtime Backup First
8.2.1 Optimal Backup Times
8.3 Comparisons of Backup First and Overtime
8.4 Database Backup Last
8.4.1 Backup Last
8.4.2 Backup Overtime Last
8.5 Problem
References
9 Which is Better Problems in Checkpoint Models
9.1 Periodic Checkpoint Model
9.2 Random Checkpoint Models
9.2.1 Two Kinds of Tasks
9.2.2 Two Kinds of Checkpoints
9.3 Two Examples
9.4 Imperfect Checkpoint Model
9.4.1 Periodic Checkpoint
9.4.2 Random Checkpoint
9.5 Problem
References
Appendix Appendix A
A.1 Properties of Failure Rate f left parenthesis t right parenthesis divided by ModifyingAbove upper F With quotation dash left parenthesis t right parenthesisf(t)/overlineF(t) for Age Replacement
A.2 Properties of Failure Rate h left parenthesis t right parenthesish(t) for Replacement with Minimal Repair
A.3 Properties of Failure Rates f left parenthesis t right parenthesis divided by ModifyingAbove upper F With quotation dash left parenthesis t right parenthesisf(t)/overlineF(t) for Periodic Replacement
A.4 Properties of Failure Rates h left parenthesis t right parenthesish(t) for Periodic Replacement
A.5 Properties of Failure Rates h left parenthesis t right parenthesish(t) for Replacement Over Failure Number
A.6 Properties of Failure Rates for Extended Replacement
A.7 Properties of Failure Rates for Shock and Damage Models
Appendix Appendix B
Index
