The performance of a reliability system can be improved by different methods, e.g. the reliability of one or more components can be improved, hot or cold redundant components can be added to the system. Sometimes these measures can be equivalent as they will have the same effect on some performance measure of the system. This paper discusses the reliability equivalences of a parallel–series system. The system considered here consists of m subsystems connected in parallel, with subsystem i consisting of ni independent and identical components in series for i=1, 2, …, m. Three different methods are used to improve the system reliability: (i) the reduction method, (ii) the hot duplication method and (iii) the cold duplication method. Each component of the system has four states and two types of partial failure rates. In this study, the lifetimes of the system components are exponentially distributed. A numerical example is introduced to illustrate how the idea of this work can be applied.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 3, Issue 3) |
| DOI | 10.11648/j.sjams.20150303.19 |
| Page(s) | 160-164 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Partial Failure Rate, Reliability Equivalence Factors, Parallel-Series System
| [1] | Abdelfattah, M. and El-Faheem Adel A.( 2014), Reliability equivalence factors of a system with mixture of n independent and non-identical lifetimes with delay time, Journal of the Egyptian Mathematical Society, 22, 96–101. |
| [2] | Burr, I. W. (1942), Cumulative frequency functions, The Annals of Mathematical Statistics, 13(2), 215-222. |
| [3] | El-Damcese, M. A. and Khalifa M. M.( 2008), Reliability equivalence factors of a series-parallel systems in Weibull distribution. International Journal of Reliability and Applications, 9(2), 153-165. |
| [4] | Migdadi, H. S. and Al-Batah, M. S.( 2014), Testing Reliability Equivalence Factors of a Series- Parallel Systems in Burr Type X Distribution, British Journal of Mathematics & Computer Science, 4(18), 2618-2629. |
| [5] | Mudholkar G.S., Srivastava D.K. (1993), Exponentiated Weibull family for analyzing bathtub failure rate data, IEEE Transactions on Reliability, 42(2),299-302. |
| [6] | Mustafa, A. and El-Faheem, A. A.( 2012), Reliability equivalence factors of a general parallel system with mixture of lifetimes. Applied Mathematical Sciences, 6(76), 3769-3784. |
| [7] | Rade, L., Reliability Equivalence, Studies in Statistical Quality Control and Reliability 1989-1, Mathematical Statistics, Chalmers University of Technology. |
| [8] | Rade, L., Reliability Systems of 3-state Components, Studies in Statistical Quality Control and Reliability 1990-3, Mathematical Statistics, Chalmers University of Technology. |
| [9] | Rade, L. Performance Measures for Reliability Systems with a Cold Standby with a Random Switch, Studies in Statistical Quality Control and Reliability 1991 , Chalmers University of Technology. |
| [10] | Rade, L. (1993a), Reliability Equivalence, Microelectronics & Reliability, 33(3), 323-325. |
| [11] | Rade, L. (1993b), Reliability Survival Equivalence, Microelectronics & Reliability, 33(6), 881-894. |
| [12] | Sarhan, A. M., Tadj, L., Al-khedhairi, A. and Mustafa, A. (2008), Equivalence Factors of a Parallel-Series System, Applied Sciences, 10, 219-230. |
| [13] | Shawky, A. I., Abdelkader, Y. H. and Al-Ohally, M. I.( 2013), Reliability equivalence factors in exponentiated exponential distribution. Wulfenia Journal, 20(3), 75-85. |
| [14] | Xia, Y. and Zhang, G.( 2007), Reliability equivalence factors in Gamma distribution. Applied Mathematics and Computation, 187(2), 567-573. |
APA Style
M. A. El-Damcese. (2015). Reliability Equivalence Analysis of a Parallel-Series System Subject to Degradation Facility. Science Journal of Applied Mathematics and Statistics, 3(3), 160-164. https://doi.org/10.11648/j.sjams.20150303.19
ACS Style
M. A. El-Damcese. Reliability Equivalence Analysis of a Parallel-Series System Subject to Degradation Facility. Sci. J. Appl. Math. Stat. 2015, 3(3), 160-164. doi: 10.11648/j.sjams.20150303.19
AMA Style
M. A. El-Damcese. Reliability Equivalence Analysis of a Parallel-Series System Subject to Degradation Facility. Sci J Appl Math Stat. 2015;3(3):160-164. doi: 10.11648/j.sjams.20150303.19
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.sjams.20150303.19,
author = {M. A. El-Damcese},
title = {Reliability Equivalence Analysis of a Parallel-Series System Subject to Degradation Facility},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {3},
number = {3},
pages = {160-164},
doi = {10.11648/j.sjams.20150303.19},
url = {https://doi.org/10.11648/j.sjams.20150303.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20150303.19},
abstract = {The performance of a reliability system can be improved by different methods, e.g. the reliability of one or more components can be improved, hot or cold redundant components can be added to the system. Sometimes these measures can be equivalent as they will have the same effect on some performance measure of the system. This paper discusses the reliability equivalences of a parallel–series system. The system considered here consists of m subsystems connected in parallel, with subsystem i consisting of ni independent and identical components in series for i=1, 2, …, m. Three different methods are used to improve the system reliability: (i) the reduction method, (ii) the hot duplication method and (iii) the cold duplication method. Each component of the system has four states and two types of partial failure rates. In this study, the lifetimes of the system components are exponentially distributed. A numerical example is introduced to illustrate how the idea of this work can be applied.},
year = {2015}
}
TY - JOUR T1 - Reliability Equivalence Analysis of a Parallel-Series System Subject to Degradation Facility AU - M. A. El-Damcese Y1 - 2015/06/08 PY - 2015 N1 - https://doi.org/10.11648/j.sjams.20150303.19 DO - 10.11648/j.sjams.20150303.19 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 160 EP - 164 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20150303.19 AB - The performance of a reliability system can be improved by different methods, e.g. the reliability of one or more components can be improved, hot or cold redundant components can be added to the system. Sometimes these measures can be equivalent as they will have the same effect on some performance measure of the system. This paper discusses the reliability equivalences of a parallel–series system. The system considered here consists of m subsystems connected in parallel, with subsystem i consisting of ni independent and identical components in series for i=1, 2, …, m. Three different methods are used to improve the system reliability: (i) the reduction method, (ii) the hot duplication method and (iii) the cold duplication method. Each component of the system has four states and two types of partial failure rates. In this study, the lifetimes of the system components are exponentially distributed. A numerical example is introduced to illustrate how the idea of this work can be applied. VL - 3 IS - 3 ER -
Information
Email: