SpringerLink
Log in

Introduction

  • Chapter
  • First Online:
Which-Is-Better (WIB): Problems in Reliability Theory

Part of the book series: Springer Series in Reliability Engineering ((RELIABILITY))

  • 102 Accesses

Abstract

It has been wellknown that Probability arose in the letter from Pascal to Fermat around 1654 on such questions as the fair division of the stakes in the game of change [1, p. 239].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
EUR 29.95
Price includes VAT (Thailand)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
EUR 139.09
Price includes VAT (Thailand)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
EUR 169.99
Price excludes VAT (Thailand)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info
Hardcover Book
EUR 169.99
Price excludes VAT (Thailand)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. David FN (1962) Games, gods, and gambling. Griffin Press, London

    Google Scholar 

  2. Barlow RE, Proschan F (1965) Mathematical theory of reliability. Wley, New York

    MATH  Google Scholar 

  3. Mizutani S, Zhao X, Nakagawa T (2021) WIB (Which-Is-Better) problems in maintenance reliability policies. In: Misra KB (ed) Handbook of advanced performability engineering. Springer, Switzerland, pp 523–547

    Chapter  Google Scholar 

  4. Nakagawa T (2005) Maintenance theory of reliability. Springer, London

    Google Scholar 

  5. Nakagawa T, Zhao X, Yun W (2011) Optimal age replacement and inspection policies with random failure and replacement times. Inter J Reliab Qual Saf Eng 18:405–416

    Article  Google Scholar 

  6. Chen M, Mizutani S, Nakagawa T (2010) Random and age replacement policies. Inter J Reliab Qual Saf Eng 17:27–39

    Article  Google Scholar 

  7. Chen, M, Nakamura S, Nakagawa T (2010). Replacement and preventive maintenance models with random working times. IEICE Trans Fund E93.A:500–507

    Google Scholar 

  8. Zhao X, Nakagawa T (2012) Optimization problems of replacement first or last in reliability theory. Euro J Oper Res 223:141–149

    Article  MathSciNet  MATH  Google Scholar 

  9. Zhao X, Nakagawa T, Zuo M (2014) Optimal replacement last with continuous and discrete policies. IEEE Trans Reliab 63:868–880

    Article  Google Scholar 

  10. Zhao X, Liu H, Nakagawa T (2015) Where does whichever occurs first hold for preventive maintenance modelings. Reliab Eng Syst Saf 142:203–211

    Article  Google Scholar 

  11. Zhao X, Al-Khalifa KN, Hamouda A, Nakagawa T (2016) First and last triggering event approaches for replacement with minimal repairs. IEEE Trans Reliab 65:197–207

    Article  Google Scholar 

  12. Mizutani S, Dong W, Zhao X, Nakagawa T (2020) Preventive replacement policies with products update announcements. Comm Stat Theory Method 49:3821–3833

    Article  MathSciNet  MATH  Google Scholar 

  13. Mizutani S, Zhao X, Nakagawa T (2021) Age and periodic replacement policies with two failure modes in general models. Reliab Eng Syst Saf 214:107754

    Article  Google Scholar 

  14. Zhao X, Cai J, Mizutani S, Nakagawa T (2021) Preventive replacement policies with time of operations, mission durations, minimal repairs and maintenance triggering approaches. J Manuf Syst 6:819–829

    Article  Google Scholar 

  15. Nakagawa T, Zhao X (2013) Comparisons of replacement policies with constant and random times. J Oper Res Japan 56:1–14

    MathSciNet  MATH  Google Scholar 

  16. Nakagawa T (2014) Random maintenance policies. Springer, London

    Book  Google Scholar 

  17. Zhao X, Al-Khalifa KN, Hamouda A, Nakagawa T (2017) Age replacement models: A summary with new perspectives and methods. Reliab Eng Syst Saf 161:95–105

    Google Scholar 

  18. Chen M, Zhao X, Nakagawa T (2019) Replacement policies with general models. Ann Oper Res 277:47–61

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhao X, Qian C, Nakamura S (2014) Age and periodic replacement models with overtime policies. Int J Reliab Qual Saf Eng 21:1450016

    Article  Google Scholar 

  20. Mizutani S, Zhao X, Nakagawa T (2015). Overtime replacement policies with finite operating interval and number. IEICE Trans Fund E98-A:2069–2076

    Google Scholar 

  21. Zhao X, Nakagawa T (2016) Over-time and over-level replacement policies with random working cycles. Ann Oper Res 244:103–116

    Article  MathSciNet  MATH  Google Scholar 

  22. Zhao X, Nakagawa T (2015) Optimal periodic and random inspection with first, last, and overtime policies. Inter J Syst Sci 46:1648–1660

    Article  MathSciNet  MATH  Google Scholar 

  23. Nakagawa T, Zhao X (2015) Maintenance overtime policies in reliability theory. Springer, London

    Google Scholar 

  24. Zhao X, Nakagawa T (2013) Comparisons of periodic and random replacement policies. In: Frenkel I et al (eds) Applied reliability engineering and risk analysis: Probilistic models and statistical inference. Wiley, pp 193–204

    Google Scholar 

  25. Zhao X, Mizutani S, Nakagawa T (2015) Which is better for replacement policlies with continuous or discrete scheduled times. Euro J Oper Res 242:477–486

    Article  MATH  Google Scholar 

  26. Zhao X, Qian C, Nakagawa T (2017) Comparisons of maintenance policies with periodic times and repair numbers. Reliab Eng Syst Saf 168:161–170

    Article  Google Scholar 

  27. Mizutani S, Zhao X, Nakagawa T (2020) Which replacement is better at working cycles or number of failures. IEICE Trans Fund E103. A:523–532

    Google Scholar 

  28. Zhao X, Al-Khalifa KN, Hamouda A, Nakagawa T (2016) What is middle maintenance policy. Qual Reliab Eng Inter 32:2403–2414

    Article  Google Scholar 

  29. Zhao X, Li B, Mizutani S, Nakagawa T (2021) A revisit of age-based replacement models with exponential failure distributions. IEEE Trans Reliab. https://doi.org/10.1109/TR.2021.3111682

    Article  Google Scholar 

  30. Zhao X, Chen M, Nakagawa T (2022) Periodic replacement policies with shortage and excess costs. Ann Oper Res 311:469–487

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhao X, Chen M, Nakagawa T (2016) Replacement policies for a parallel system with shortage and excess costs. Reliab Eng Syst Saf 150:89–95

    Article  Google Scholar 

  32. Zhao X, Mizutani S, Chen M, Nakagawa T (2022) Preventive replacement policies for parallel systems with deviation costs between replacement and failure. Ann Oper Res 312:533–551

    Article  MathSciNet  MATH  Google Scholar 

  33. Wang J, Zhao X, **ang J (2022) Optimum design and replacement policies for \(k\)-out-of-\(n\) systems with deviation time and cost. Ann Oper Res. https://doi.org/10.1007/s10479-022-05043-1

    Article  Google Scholar 

  34. Nakagawa T (2008) Advanced reliability models and maintenance policies. Springer, London

    Google Scholar 

  35. Nakagawa T, Zhao X (2012) Optimization problems of a parallel system with a random number of units. IEEE Trans Reliab 61:543–548

    Article  Google Scholar 

  36. Ito K, Zhao X, Nakagawa T (2017) Random number of units for \(K\)-out-of-\(n\) systems. App Mathl Model 45:563–572

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhao X, Chen M, Nakagawa T (2016) Comparisons of standby and parallel systems in reliability, replacement, scheduling and application. Proc Inst Mech Eng Part O: J Risk Reliab 230:101–108

    Google Scholar 

  38. Nakagawa T (2007) Shock and damage models in reliability theory. Springer, London

    MATH  Google Scholar 

  39. Zhao X, Nakagawa T (2018) Advanced maintenance policies for shock and damage models. Springer, Switzerland

    Book  Google Scholar 

  40. Zhao X, Qian CH, Nakagawa T (2013) Optimal policies for cumulative damage models with maintenance last and first. Reliab Eng Syst Saf 110:50–59

    Article  Google Scholar 

  41. Zhao X, Nakamura S, Nakagawa T (2013) Optimal maintenance policies for cumulative damage models with random working times. J Qual Maint Eng 19:25–37

    Article  Google Scholar 

  42. Zhao X, Qian C, Sheu S (2014) Cumulative damage models with random working times. In: Nakamura S, Qian C, Chen M (eds) Reliability modeling with applications. World Scientific, pp 79–98

    Google Scholar 

  43. Nakamura S, Zhao X, Nakagawa T (2017) Constant and random full backup models with incremental and differential backup schemes. Inter J Reliab Qual Saf Eng 24:1750015

    Article  Google Scholar 

  44. Zhao X, Nakamura S, Qian C, Sheu S (2017) Cumulative backup policies for database systems. In: Nakamura S, Qian C, Nakagawa T (eds) Reliability modeling with computer and maintenance applications. World Scientific, pp 235–254

    Google Scholar 

  45. Zhao X, Wang D, Mizutani S, Nakagawa T (2022) Data backup policies with failure-oblivious computing in reliability theory. Ann Oper Res. https://doi.org/10.1007/s10479-022-04941-8

    Article  Google Scholar 

  46. Naruse K, Nakagawa T (2020) Optimal checking intervals, schemes and structures for computing modules. In: Pham H (ed) Reliability and statistical computing. Springer, London, pp 265–287

    Google Scholar 

  47. Zhao X, Nakamura S, Nakagawa T (2011) Two generational garbage collection models with major collection time. IEICE Trans Fund E94-A:1558–1566

    Google Scholar 

  48. Chen M, Zhao X, Nakamura S (2014) Periodic and random inspections for a computer system. In: Nakamura S, Qian C, Chen M (eds) Reliability modeling with applications. World Scientific, pp 249–267

    Google Scholar 

  49. Zhao X, Zheng Q, Jia X, Qian C, Mizutani S, Chen M (2022) Periodic and sequential inspection policies with mission failure probabilities. Qual Reliab Eng Inter 38:1539–1557

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Business Administration, Aichi Institute of Technology, Toyota, Aichi, Japan

    Satoshi Mizutani

  2. College of Economics and Management, Nan**g University of Aeronautics and Astronautics, Nan**g, China

    Xufeng Zhao

  3. Department of Business Administration, Aichi Institute of Technology, Toyota, Aichi, Japan

    Toshio Nakagawa

Authors
  1. Satoshi Mizutani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xufeng Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Toshio Nakagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Satoshi Mizutani .

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Mizutani, S., Zhao, X., Nakagawa, T. (2023). Introduction. In: Which-Is-Better (WIB): Problems in Reliability Theory. Springer Series in Reliability Engineering. Springer, Cham. https://doi.org/10.1007/978-3-031-27316-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-27316-2_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-27315-5

  • Online ISBN: 978-3-031-27316-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation