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Availability and cost-benefit evaluation for a repairable retrial system with warm standbys and priority

Jia Kang ,

School of Science, Yanshan University, Qinhuangdao, People's Republic of China

Linmin Hu ,

School of Science, Yanshan University, Qinhuangdao, People's Republic of China

Rui Peng ,

School of Economics and Management, Beijing University of Technology, Beijing, People's Republic of China

Yan Li ,

School of Science, Hebei University of Science and Technology, Shijiazhuang, People's Republic of China

Ruiling Tian

School of Science, Yanshan University, Qinhuangdao, People's Republic of China

Pages | Received 24 May. 2022, Accepted 21 Nov. 2022, Published online: 05 Dec. 2022,
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This paper investigates a warm standby repairable retrial system with two types of components and a single repairman, where type 1 components have priority over type 2 in use. Failure and repair times for each type of component are assumed to be exponential distributions. The retrial feature is considered and the retrial time of each failed component is exponentially distributed. By using Markov process theory and matrix-analytic method, the system steady-state probabilities are derived, and the system steady-state availability and some steady-state performance indices are obtained. Using the Bayesian approach, the system parameters can be estimated. The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states. Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.

  • Amari, S. V., Pham, H., & Misra, R. B. (2012). Reliability characteristics of k-out-of-n warm standby systems. IEEE Transactions on Reliability61(4), 1007–1018.
  • Chen, W. L., & Wang, K. H. (2018). Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy. Reliability Engineering & System Safety180, 476–486. 
  • El-Damcese, M. A. (2009). Analysis of warm standby systems subject to common-cause failures with time varying failure and repair rates. Applied Mathematical Sciences3(18), 853–860. 
  • Gao, S (2021). Availability and reliability analysis of a retrial system with warm standbys and second optional repair service. Communications in Statistics-Theory and Methods1–19.
  • Gao, S., & Wang, J (2021). Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility. Reliability Engineering & System Safety205, 107240. 
  • Hsu, Y. L., Lee, S. L., & Ke, J. C (2009). A repairable system with imperfect coverage and reboot: Bayesian and asymptotic estimation. Mathematics and Computers in Simulation79(7), 2227–2239. 
  • Janssens, G. K (1997). The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network. IEEE Transactions on Communications45(3), 360–364. 
  • Ke, J. C., Yang, D. Y., S. H. Sheu, & Kuo, C. C (2013). Availability of a repairable retrial system with warm standby components. International Journal of Computer Mathematics90(11), 2279–2297. 
  • Krishnamoorthy, A., & Ushakumari, P. V (1999). Reliability of a k-out-of-n system with repair and retrial of failed units. Top7(2), 293–304. 
  • Kumar, P., & Jain, M (2020). Reliability analysis of a multi-component machining system with service interruption, imperfect coverage, and reboot. Reliability Engineering & System Safety202, 106991. 
  • Kuo, C. C., Sheu, S. H., Ke, J. C., & Zhang, Z. G (2014). Reliability-based measures for a retrial system with mixed standby components. Applied Mathematical Modelling38(19-20), 4640–4651. 
  • Levitin, G., Finkelstein, M., & Dai, Y (2021). Optimal shock-driven switching strategies with elements reuse in heterogeneous warm-standby systems. Reliability Engineering & System Safety210, 107517. 
  • Meena, R. K., Jain, M., Sanga, S. S., & Assad, A (2019). Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation. Applied Mathematics and Computation361, 858–873. 
  • Pustova, S. V (2010). Investigation of call centers as retrial queuing systems. Cybernetics and Systems Analysis46(3), 494–499. 
  • She, J., & Pecht, M. G (1992). Reliability of a k-out-of-n warm-standby system. IEEE Transactions on Reliability41(1), 72–75. 
  • Singh, J (1989). A warm standby redundant system with common cause failures. Reliability Engineering & System Safety26(2), 135–141. 
  • Srinivasan, S. K., & Subramanian, R (2006). Reliability analysis of a three unit warm standby redundant system with repair. Annals of Operations Research143(1), 227–235. 
  • Tran-Gia, P., & Mandjes, M (1997). Modeling of customer retrial phenomenon in cellular mobile networks. IEEE Journal on Selected Areas in Communications15(8), 1406–1414. 
  • Wang, G., Hu, L., Zhang, T., & Wang, Y (2021). Reliability modeling for a repairable (k1k1, k2k2)-out-of-n: G system with phase-type vacation time. Applied Mathematical Modelling91, 311–321.
  • Wang, J., & Zhang, F (2016). Monopoly pricing in a retrial queue with delayed vacations for local area network applications. IMA Journal of Management Mathematics27(2), 315–334. 
  • Wu, C. H., Yen, T. C., & Wang, K. H (2021). Availability and comparison of four retrial systems with imperfect coverage and general repair times. Reliability Engineering & System Safety212, 107642. 
  • Wu, X., Hillston, J., & Feng, C (2016). Availability modeling of generalized k-out-of-n: G warm standby systems with PEPA. IEEE Transactions on Systems, Man, and Cybernetics: Systems47(12), 3177–3188. 
  • Yang, D. Y., & Tsao, C. L (2019). Reliability and availability analysis of standby systems with working vacations and retrial of failed components. Reliability Engineering & System Safety182, 46–55. 
  • Yen, T. C., & Wang, K. H (2020). Cost benefit analysis of four retrial systems with warm standby units and imperfect coverage. Reliability Engineering & System Safety202, 107006. 
  • Yen, T. C., Wang, K. H., & Wu, C. H (2020). Reliability-based measure of a retrial machine repair problem with working breakdowns under the F-policy. Computers & Industrial Engineering150, 106885. 
  • Zhang, T., & Horigome, M. (2000). Availability of 3-out-of-4: G warm standby system. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences83(5), 857–862. 
  • Zhang, T., Xie, M., & Horigome, M (2006). Availability and reliability of k-out-of-(m+n): G warm standby systems. Reliability Engineering & System Safety91(4), 381–387. 
  • Zhao, X., Guo, X., & Wang, X (2018). Reliability and maintenance policies for a two-stage shock model with self-healing mechanism. Reliability Engineering & System Safety172, 185–194. 
  • Zhao, X., Wang, S., Wang, X., & Cai, K (2018). A multi-state shock model with mutative failure patterns. Reliability Engineering & System Safety178, 1–11.
  • Zhao, X., Wu, C., Wang, X., & Sun, J (2020). Reliability analysis of k-out-of-n: F balanced systems with multiple functional sectors. Applied Mathematical Modelling82, 108–124.

To cite this article: Jia Kang, Linmin Hu, Rui Peng, Yan Li & Ruiling Tian (2023) Availability and cost-benefit evaluation for a repairable retrial system with warm standbys and priority, Statistical Theory and Related Fields, 7:2, 164-175, DOI: 10.1080/24754269.2022.2152591

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