Skip to main content
SpringerLink
Log in

Probabilistic Analysis of Performance Measures of Redundant Systems Under Weibull Failure and Repair Laws

  • Conference paper
  • First Online:
Computing and Network Sustainability

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 12))

Abstract

The aim of the present paper is to analyze probabilistically various performance measures of two redundant systems under Weibull failure and repair activities using semi-Markov processes and regenerative point technique. Two stochastic models comprise of one original and one duplicate units are developed with the provision of a single repair facility and priority. All repairs and preventive maintenance, after a pre-specific time, are perfect. Recurrence relations of availability, mean time to system failure and profit function for both the models are derived. To highlight the importance of the system, numerical and graphical results for the difference of both models are obtained with respect to failure rate of original unit.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Cao J, Wu Y (1989) Reliability analysis of a two-unit cold standby system with a replaceable repair facility. Microelectron Reliab 29(2):145–150

    Article  Google Scholar 

  2. Chandrasekhar P, Natarajan R, Yadavalli VSS (2004) A study on a two unit standby system with Erlangian repair time. Asia-Pac J Oper Res 21(03):271–277

    Article  MathSciNet  MATH  Google Scholar 

  3. Goel LR, Sharma SC (1989) Stochastic analysis of a 2-unit standby system with two failure modes and slow switch. Microelectron Reliab 29(4):493–498

    Article  Google Scholar 

  4. Gupta R, Kumar P, Gupta A (2013) Cost-benefit analysis of a two dissimilar unit cold standby system with Weibull failure and repair laws. Int J Syst Assur Eng Manage 4(4):327–334

    Article  Google Scholar 

  5. Kumar A, Malik SC (2012) Reliability modeling of a computer system with priority to s/w replacement over h/w replacement subject to MOT and MRT. Int J Pure Appl Math 80(5):693–709

    Google Scholar 

  6. Kumar A, Saini M (2014) Cost-benefit analysis of a single-unit system with preventive maintenance and Weibull distribution for failure and repair activities. J Appl Math Stat Inform 10(2):5–19

    MathSciNet  MATH  Google Scholar 

  7. Kumar A, Saini M, Devi K (2016) Analysis of a redundant system with priority and Weibull distribution for failure and repair. Cogent Math 3(1):1–11

    MathSciNet  Google Scholar 

  8. Kishan R, Jain D (2014) Classical and Bayesian analysis of reliability characteristics of a two-unit parallel system with Weibull failure and repair laws. Int J Syst Assur Eng Manage 5(3):252–261

    Article  Google Scholar 

  9. Mahmoud MAW, Moshref ME (2010) On a two-unit cold standby system considering hardware, human error failures and preventive maintenance. Math Comput Model 51(5):736–745

    Article  MathSciNet  MATH  Google Scholar 

  10. Moghaddass R, Zuo MJ, Qu J (2011) Reliability and availability analysis of a repairable-out-of-system with repairmen subject to shut-off rules. IEEE Trans Reliab 60(3):658–666

    Article  Google Scholar 

  11. Wu Q, Wu S (2011) Reliability analysis of two-unit cold standby repairable systems under Poisson shocks. Appl Math Comput 218(1):171–182

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Automobile Engineering, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Indeewar Kumar

  2. Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Ashish Kumar, Monika Saini & Kuntal Devi

Authors
  1. Indeewar Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ashish Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Monika Saini
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kuntal Devi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ashish Kumar .

Editor information

Editors and Affiliations

  1. Department of Software and Systems Engineering, VIT University, Vellore, Tamil Nadu, India

    H.R . Vishwakarma

  2. Department of Electronics and Communication Engineering, ITM University, Gwalior, Madhya Pradesh, India

    Shyam Akashe

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer Nature Singapore Pte Ltd.

About this paper

Cite this paper

Kumar, I., Kumar, A., Saini, M., Devi, K. (2017). Probabilistic Analysis of Performance Measures of Redundant Systems Under Weibull Failure and Repair Laws. In: Vishwakarma, H., Akashe, S. (eds) Computing and Network Sustainability. Lecture Notes in Networks and Systems, vol 12. Springer, Singapore. https://doi.org/10.1007/978-981-10-3935-5_2

Download citation

  • DOI: https://doi.org/10.1007/978-981-10-3935-5_2

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-3934-8

  • Online ISBN: 978-981-10-3935-5

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation