Which-Is-Better (WIB): Problems in Reliability Theory

ISBN-13: 9783031273155 / Angielski / Twarda / 2023 / 240 str.

Satoshi Mizutani; Xufeng Zhao; Toshio Nakagawa

Opis

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.

Spis treści

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 Problems 

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 Problems 

References 

Appendix A: Extended Failure Rates References 

A.1 Properties of Failure Rate f(t)/F(t) for Age Replacement 

A.2 Properties of Failure Rate h(t) for Replacement with Minimal

Repair

A.3 Properties of Failure Rates f(t)/F(t) for Periodic Replacement 

A.4 Properties of Failure Rates h(t) for Periodic Replacement

A.5 Properties of Failure Rates h(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 

References 

Appendix B: Answer to Selected Problesms 

Index 

O autorze

Dr. Satoshi Mizutani has interests of optimal maintenance policies in reliability theory such as inspection policy for computer systems and replacement policy for natural disaster. He has shown the several numerical examples of optimal replacement and checking times. His research for optimal maintenance and inspection policies has been published in Reliability Engineering & System Safety, International Journal of Reliability, Quality and Safety Engineering, Computers & Mathematics with Applications, and so on. Dr. Mizutani is a member of Nagoya Computer and Reliability Research organized by Professor Toshio Nakagawa in Japan.

Professor Xufeng Zhao is interested in probability theory, stochastic process, reliability and maintenance theory, and applications in computer and industrial systems. He has published two books in maintenance theory from Springer and more than seventy research papers in peer-reviewed journals, and he is the author or co-author of twelve chapters from Springer and Wiley, etc. He has obtained one best paper award from IEEE Reliability Society Japan Chapter and five best paper awards from international conferences in reliability, maintainability, and quality. Professor Zhao serves as an associate editor for Stochastic Models, that is an affiliated publication of INFORMS, and the editorial board and guest editors of other journals. He also severs as a program chair for ISSAT International Conference on Reliability and Quality in Design.

Professor Toshio Nakagawa has already published more than two hundred research papers on subject of maintenance and reliability theory in main reliability journals and has published five books titled on “Maintenance Theory in Reliability” in 2005, “Shock and Damage Models in Reliability Theory” in 2007, “Advanced Reliability Models and Maintenance Policies” in 2008, “Stochastic Processes with Applications to Reliability Theory” in 2011, “Random Maintenance Policies” in 2014 from Springer, and so on. His research group in Nagoya has continuously studied reliability and maintenance theory and their applications since 1988 and has published a large number of papers in reliability journals and at international conferences.