Reliability of an engineering system characterized by hot and cold standby: A compound boundary value problem

Authors

  • Edmond Vanderperre Reliability Engineering Research Unit, Blankenberge, Belgium
  • Stanislav Makhanov School of Information and Computer Technology, Sirindhorn International Institute of Technology, Thammasat University, T. Bangkadi, A. Muang, Pathum Thani, Thailand

DOI:

https://doi.org/10.2298/YJOR200815016V

Keywords:

Duplex System, Priority Rule, Stopping Time, Survival Function

Abstract

We analyse the reliability (survival function) of a duplex system characterized by hot standby and sustained by an auxiliary unit in cold standby. The entire system is attended by two heterogeneous repairmen. Our methodology is based on the theory of sectionally holomorphic functions combined with the notion of dual transforms. Finally, we also study the total occupational time of the repairman responsible for the repair of the failed priority unit during the survival time of the system.

References

Apostol, T. M. (1978). "Mathematical Analysis", Addison-Wesley, Addison-Wesley series in mathematics, London.

Birolini, A. (2007). "Reliability Engineering, Theory and Practice", Springer, Berlin.

Brémaud, P. (1981). "Point processes and queues, Martingale dynamics", Springer Series in Statistics, Springer, New York, NY.

Cox, D. R. (1955). "A use of complex probabilities in the theory of stochastic processes", Mathematical Proceedings of the Cambridge Philosophical Society, 2(51), 313–319.

Doob, J. L. (1994). "Measure Theory", Springer, Berlin.

Epstein, B., & Weissmann, I. (2008). "Mathematical Models for System Reliability", Chapman and Hall, CRC Press, Baton Rouge.

Fenyö, S., & Stolle, H. W. (1982). "Theorie und Praxis der Linearen Integralgleichungen", Birkhäuser Verlag, Basel.

Gakhov, L. D. (1996). "Boundary Value Problems", Pergamon Press, Oxford.

Gnedenko, B. V., & Ushakov, I. A. (1995). "Probabilistic Reliability Engineering", John Wiley & Sons, N.Y.C.

Kim, D. S., Lee, S. M., Jung, J.-H., Kim, T. H., Lee, S. P., & Jong, S. (2012). "Reliability and availability analysis for an on-board computer in a satellite system using standby redundancy and rejuvenation", Journal of Mechanical Science and Technology, 7(26), 2059-2063.

Lu, J.-K. (1993). "Boundary Value Problems for Analytic Functions", World Scientific, Hong Kong, Series in Pure Mathematics.

Pólya, G., & Szegö, I. (1978). "Problems and Theorems in Analysis", Springer, Berlin.

Roos, B. W. (1996). "Analytic Functions and Distributions in Physics and Engineering", John Wiley & Sons, N.Y.C.

Marcos, L., Hoffmann, S., da Costa, C. A., de Oliveira Ramos, G., & da Rosa Righi, R. (2020). "A survey on decision-making based on system reliability in the context of Industry 4.0", Journal of Manufacturing Systems, 56, 133-156.

Serfozo, R. F. (1990). "Point processes", Stochastic Models Handbooks in Operations Research and Management Science, Elsevier, 2, 1-93.

Goodman, J. W. (2020). "Fourier Transforms using Mathematica", SPIE Digital Library.

Ushakov, I. A. (2012). "Stochastic Reliability Models", John Wiley & Sons, N.Y.C.

Vanderperre, E. J. (2000). "Long-run availability of a two-unit standby system subjected to a priority rule", Bulletin of the Belgian Mathematical Society-Simon Stevin, 3(7), 355-364.

Vanderperre, E. J., & Makhanov, S. S. (2014). "On the availability of a warm standby system: a numerical approach", TOP, 2(22), 644-657.

Vanderperre, E. J., & Makhanov, S. S. (2014). "Reliability analysis of a repairable duplex system", International Journal of Systems Science, 9(45), 1970-1977.

Vanderperre, E. J., & Makhanov, S. S. (2017). "A functional equation related to a repairable system subjected to priority rules", European Journal of Applied Mathematics, 1(28), 123–140.

Downloads

Published

2021-08-01

Issue

Section

Research Articles