Skip to main content
SpringerLink
Log in

Stochastic behavior of dissimilar units cold standby system waiting for repair

  • Original Research
  • Published:
Life Cycle Reliability and Safety Engineering Aims and scope Submit manuscript

Abstract

Investigation of the time behavior of repairable systems spans a very large class of stochastic processes. The repetition of the same events connects the theory of reliability with Markov and semi-Markov processes. Exploiting this theory, the present study deals with two repairable dissimilar units’ cold standby system waiting for repair facility after failure of system units. Also, the regenerative point technique has been employed to obtain various reliability measures for the assumed system. Next, a particular case with exponential failures, arbitrary waiting and arbitrary repair rate is simulated followed by conclusions in the last section.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • 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 

  • El-Said KM, El-Sherbeny MS (2010) Stochastic analysis of a two-unit cold standby system with two-stage repair and waiting time. Sankhya B 72(1):1–10

    Article  MathSciNet  MATH  Google Scholar 

  • Eryilmaz S, Tank F (2012) On reliability analysis of a two-dependent-unit series system with a standby unit. Appl Math Comput 218(15):7792–7797

    MathSciNet  MATH  Google Scholar 

  • Ghitany ME, Atieh B, Nadarajah S (2008) Lindley distribution and its application. Math Comput Simul 78(4):493–506

    Article  MathSciNet  MATH  Google Scholar 

  • Ionescu DE, Limnios N (1999) Statistical and probabilistic models in reliability. Springer, New York

    Book  Google Scholar 

  • Jia J, Wu S (2009) Optimizing replacement policy for a cold-standby system with waiting repair times. Appl Math Comput 214(1):133–141

    MathSciNet  MATH  Google Scholar 

  • Jia X, Chen H, Cheng Z, Guo B (2016) A comparison between two switching policies for two-unit standby system. Reliab Eng Syst Saf 148:109–118

    Article  Google Scholar 

  • Liu B, Cui L, Wen Y, Shen J (2015) A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process. Reliab Eng Syst Saf 142:1–8

    Article  Google Scholar 

  • Manglik M, Ram M (2013) Reliability analysis of a two unit cold standby system using Markov process. J Reliab Stat Stud 6(2):65–80

    Google Scholar 

  • Pundir PS, Patawa R, Gupta PK (2018) Stochastic outlook of two non-identical unit parallel system with priority in repair. Cogent Math Stat 5:1467208

    Article  MathSciNet  Google Scholar 

  • Ram M, Singh SB, Singh VV (2013) Stochastic analysis of a standby system with waiting repair strategy. IEEE Trans Syst Man Cybern: Syst 43(3):698–707

    Article  Google Scholar 

  • Srinivasan SK, Gopalan MN (1973) Probabilistic analysis of a 2-unit cold-standby system with a single repair facility. IEEE Trans Reliab 22(5):250–254

    Article  MathSciNet  Google Scholar 

  • Subramanian R, Venkatakrishnan KS, Kistner KP (1976) Reliability of a repairable system with standby failure. Oper Res 24(1):169–176

    Article  MathSciNet  MATH  Google Scholar 

  • Yang DY, Tsao CL (2018) Reliability and availability analysis of standby systems with working vacations and retrial of failed components. Reliab Eng Syst Saf. https://doi.org/10.1016/j.ress.2018.09.020

    Google Scholar 

  • Zhang YL, Wang GJ (2007) A deteriorating cold standby repairable system with priority in use. Eur J Oper Res 183(1):278–295

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics, University of Allahabad, Allahabad, India

    Pramendra Singh Pundir & Rohit Patawa

Authors
  1. Pramendra Singh Pundir
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rohit Patawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rohit Patawa.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pundir, P.S., Patawa, R. Stochastic behavior of dissimilar units cold standby system waiting for repair. Life Cycle Reliab Saf Eng 8, 43–53 (2019). https://doi.org/10.1007/s41872-018-00070-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s41872-018-00070-z

Keywords

Mathematics Subject Classification

Search

Navigation