Advertisement

Stochastic behavior of dissimilar units cold standby system waiting for repair

  • Pramendra Singh Pundir
  • Rohit PatawaEmail author
Original Research
  • 20 Downloads

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.

Keywords

MTSF Profit function Exponential Lindley Availability Maintenance 

Mathematics Subject Classification

90B25 37A50 44A10 91B70 

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):145–150CrossRefGoogle Scholar
  2. 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):1–10MathSciNetCrossRefzbMATHGoogle Scholar
  3. Eryilmaz S, Tank F (2012) On reliability analysis of a two-dependent-unit series system with a standby unit. Appl Math Comput 218(15):7792–7797MathSciNetzbMATHGoogle Scholar
  4. Ghitany ME, Atieh B, Nadarajah S (2008) Lindley distribution and its application. Math Comput Simul 78(4):493–506MathSciNetCrossRefzbMATHGoogle Scholar
  5. Ionescu DE, Limnios N (1999) Statistical and probabilistic models in reliability. Springer, New YorkCrossRefGoogle Scholar
  6. Jia J, Wu S (2009) Optimizing replacement policy for a cold-standby system with waiting repair times. Appl Math Comput 214(1):133–141MathSciNetzbMATHGoogle Scholar
  7. Jia X, Chen H, Cheng Z, Guo B (2016) A comparison between two switching policies for two-unit standby system. Reliab Eng Syst Saf 148:109–118CrossRefGoogle Scholar
  8. 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 142:1–8CrossRefGoogle Scholar
  9. Manglik M, Ram M (2013) Reliability analysis of a two unit cold standby system using Markov process. J Reliab Stat Stud 6(2):65–80Google Scholar
  10. Pundir PS, Patawa R, Gupta PK (2018) Stochastic outlook of two non-identical unit parallel system with priority in repair. Cogent Math Stat 5:1467208MathSciNetCrossRefGoogle Scholar
  11. 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):698–707CrossRefGoogle Scholar
  12. Srinivasan SK, Gopalan MN (1973) Probabilistic analysis of a 2-unit cold-standby system with a single repair facility. IEEE Trans Reliab 22(5):250–254MathSciNetCrossRefGoogle Scholar
  13. Subramanian R, Venkatakrishnan KS, Kistner KP (1976) Reliability of a repairable system with standby failure. Oper Res 24(1):169–176MathSciNetCrossRefzbMATHGoogle Scholar
  14. 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
  15. Zhang YL, Wang GJ (2007) A deteriorating cold standby repairable system with priority in use. Eur J Oper Res 183(1):278–295CrossRefzbMATHGoogle Scholar

Copyright information

© Society for Reliability and Safety (SRESA) 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of AllahabadAllahabadIndia

Personalised recommendations