Improving the Performance of a Series-Parallel System Based on Gamma Distribution

Main Article Content

Abdelfattah Mustafa

Abstract

The performance of a series-parallel system is improved by using the reliability equivalence factors technique. The lifetimes of the components are assumed to be gamma distributed. The system reliability is improved by using three different methods: (i) Reduction method, (ii) Hot duplication method, (iii) Cold duplication method. The reliability function and mean time to failure for each method are derived. Finally, the numerical application is introduced.

Article Details

References

  1. A.H. Abdel-Hamid, A.F. Hashem, A New Lifetime Distribution for a Series-Parallel System: Properties, Applications and Estimations Under Progressive Type-II Censoring, J. Stat. Comput. Simul. 87 (2016), 993–1024. https://doi.org/10.1080/00949655.2016.1243683.
  2. J.M. Alghazo, A. Mustafa, A.A. El-Faheem, Availability Equivalence Analysis for the Simulation of Repairable Bridge Network System, Complexity. 2020 (2020), 4907895. https://doi.org/10.1155/2020/4907895.
  3. M.S. Moustafa, Reliability Model of Series-Parallel Systems, Microelectron. Reliab. 34 (1994), 1821–1823. https://doi.org/10.1016/0026-2714(94)90136-8.
  4. A. Mustafa, Reliability Equivalence Factor of n-Components Series System With Non-Constant Failure Rates, Int. J. Reliab. Appl. 10 (2009), 43–58.
  5. A. Mustafa, Reliability Equivalence of Some Systems With Mixture Weibull Failure Rates, Afr. J. Math. Computer Sci. Res. 2 (2009), 6–13.
  6. A. Mustafa, Improving the Reliability of a Series-Parallel System Using Modified Weibull Distribution, Int. Math. Forum. 12 (2017), 257–269. https://doi.org/10.12988/imf.2017.611155.
  7. A. Mustafa, Improving the Bridge Structure by Using Linear Failure Rate Distribution, J. Appl. Stat. 47 (2019), 1423–1438. https://doi.org/10.1080/02664763.2019.1679098.
  8. A. Mustafa, A.H. El-Bassoiuny, Reliability Equivalence of Some Systems With Mixture Linear Increasing Failure Rates, Pak. J. Stat. 25 (2009), 149–163.
  9. A. Musttaf, A.A. El-Faheem, Reliability Equivalence Factors of a System With m Non-Identical Mixed of Lifetimes, Amer. J. Appl. Sci. 8 (2011), 297–302. https://doi.org/10.3844/ajassp.2011.297.302.
  10. A. Mustafa, A.A. El-Faheem, Reliability Equivalence Factors of a System With 2 Non-Identical Mixed Lifetimes and Delayed Time, J. Math. Stat. 7 (2011), 169–176. https://doi.org/10.3844/jmssp.2011.169.176.
  11. A. Mustafa, B.S. El-Desouky, M. El-Dawoody, Reliability Equivalence Factors of Non-Identical Components Series System With Mixture Failure Rates, Int. J. Reliab. Appl. 10 (2009), 17–32.
  12. A. Mustafa, B.S. El-Desouky, A. Taha, Evaluating and Improving System Reliability of Bridge Structure Using Gamma Distribution, Int. J. Reliab. Appl. 17 (2016), 121–135.
  13. A. Mustafa, B.S. El-Desouky, A. Taha, Improving the Performance of the Series Parallel System With Linear Exponential Distribution, Int. Math. Forum. 11 (2016), 1037–1052. https://doi.org/10.12988/imf.2016.67107.
  14. L. Råde, Reliability Equivalence: Studies in Statistical Quality Control and Reliability, Mathematical Statistics, Chalmers University of Technology, Gothenburg, Sweden, 1989.
  15. L. Råde, Reliability equivalence, Microelectron. Reliab. 33 (1993), 323–325. https://doi.org/10.1016/0026-2714(93)90020-y.
  16. L. Råde, Reliability Survival Equivalence, Microelectron. Reliab. 33 (1993), 881–894. https://doi.org/10.1016/0026-2714(93)90261-v.
  17. A. Sarhan, Reliability Equivalence of Independent and Non-Identical Components Series Systems, Reliab. Eng. Syst. Safe. 67 (2000), 293–300. https://doi.org/10.1016/s0951-8320(99)00069-1.
  18. A.M. Sarhan, Reliability Equivalence Factors of a Parallel System, Reliab. Eng. Syst. Safe. 87 (2005), 405–411. https://doi.org/10.1016/j.ress.2004.07.008.
  19. A.M. Sarhan, Reliability Equivalence Factors of a General Series-parallel System, Reliab. Eng. Syst. Safe. 94 (2009), 229–236. https://doi.org/10.1016/j.ress.2008.02.021.
  20. A.M. Sarhan and A. Mustafa, Reliability Equivalence of a Series System Consists of n Independent and NonIdentical Components, Int. J. Reliab. Appl. 7 (2006), 111–125.
  21. A.M. Sarhan, A.S. Al-Ruzaiza, I.A. Alwasel, A.I. El-Gohary, Reliability Equivalence of a Series-Parallel System, Appl. Math. Comput. 154 (2004), 257–277. https://doi.org/10.1016/s0096-3003(03)00709-4.
  22. A.M. Sarhan, L. Tadj, A. Al-Khodari, A. Mustafa, Equivalence Factors of a Parallel-Series System, Appl. Sci. 10 (2008), 219–230.
  23. Y. Xia, G. Zhang, Reliability Equivalence Factors in Gamma Distribution, Appl. Math. Comput. 187 (2007), 567–573. https://doi.org/10.1016/j.amc.2006.07.016.
  24. Z.H. Wang, Reliability Engineering Theory and Practice, Quality Control Society of Republic of China, Taipei, 1992.