Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility

Neama Salah Youssef Temraz

doi:doi:10.11648/j.ijssam.20180301.12

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Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility

Neama Salah Youssef Temraz

Published in International Journal of Systems Science and Applied Mathematics (Volume 3, Issue 1)

Received: 22 May 2018 Accepted: 14 June 2018 Published: 13 July 2018

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Abstract

In this paper, analysis of a system consists of two dependent components with degradation facility and load sharing is introduced. The system is considered to be consisted of two components connected in parallel and works dependently where the failure of any component affects the failure of the other one. In addition, it is assumed that there is a common failure between the two components. All failure and repair rates are assumed to be constant follow bivariate exponential distribution. Markov models are used to construct the mathematical model of the system. Analysis of the availability function and steady-state availability of the model is discussed. Reliability and mean time to failure for the system is introduced. A numerical example is given for illustration.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 3, Issue 1)
DOI	10.11648/j.ijssam.20180301.12
Page(s)	10-15
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), 2018. Published by Science Publishing Group

Keywords

Bivariate Exponential Distribution, Availability, Steady State Availability, Reliability, Mean Time to Failure, Markov Models, Load-Sharing Models, Degradation

References

[1]	Barlow R. E. and Prochan F., Statistical Theory of Reliability and Life Testing: Probability Models, Silver Spring, 1981.
[2]	Meeker W. Q. and Escobar L. A., Statistical Methods for Reliability Data, Wiley, New York, 1998.
[3]	Lawless J. F., Statistical Models and Methods for Lifetime Data, John Wiley & Sons, 1982.
[4]	Misra K. B., Handbook of Performability Engineering, Springer-Verlag, London, 2008.
[5]	Balakrishnan N. and Lai C. D., Continuous Bivariate Distributions, Springer, New York, 2009.
[6]	Marshall A. W. and Olkin I., A Multivariate Exponential Distribution, Journal of American Statistical Association, 62, 30–44, 1967.
[7]	Freund J. E., A Bivariate Extension of the Exponential Distribution, Journal of American Statistical Association, 56, 971–977, 1961.
[8]	Bailey N. T. J., The Elements of Stochastic Processes, Wiley, New York, 1964.
[9]	Huang L. and Xu Q., Lifetime Reliability for Load-Sharing Redundant Systems with Arbitrary Failure Distributions, IEEE Transactions on Reliability, 59, 2, 2010.
[10]	Temraz, N. S., Availability and Reliability Analysis for System with Bivariate Weibull Lifetime Distribution, International Journal of Scientific & Engineering Research, 8(2), 376-389, 2017.
[11]	El-Damcese M. A. and Temraz N. S., Analysis for Parallel Repairable System with Degradation Facility, American Journal of Mathematics and Statistics, 2(4), 70-74, 2012.
[12]	Rausand M. and Høyland A., System Reliability Theory: Models, Statistical Methods, and Applications, Wiley, Hoboken, 2004.
[13]	Pukite P. and Pukite J., Modeling for Reliability Analysis, IEEE, New York, 1998.
[14]	Block H. W. and Basu A. P., A Continuous Bivariate Exponential Extension, Journal of American Statistical Association, 69, 1031–1037, 1974.
[15]	Walpole, Ronald E., Myers, and Raymond H., Probability and Statistics for Engineers and Scientists, Macmillan Publishing Company, 1985.

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APA Style

Neama Salah Youssef Temraz. (2018). Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. International Journal of Systems Science and Applied Mathematics, 3(1), 10-15. https://doi.org/10.11648/j.ijssam.20180301.12

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ACS Style

Neama Salah Youssef Temraz. Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. Int. J. Syst. Sci. Appl. Math. 2018, 3(1), 10-15. doi: 10.11648/j.ijssam.20180301.12

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AMA Style

Neama Salah Youssef Temraz. Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. Int J Syst Sci Appl Math. 2018;3(1):10-15. doi: 10.11648/j.ijssam.20180301.12

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@article{10.11648/j.ijssam.20180301.12,
  author = {Neama Salah Youssef Temraz},
  title = {Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {10-15},
  doi = {10.11648/j.ijssam.20180301.12},
  url = {https://doi.org/10.11648/j.ijssam.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20180301.12},
  abstract = {In this paper, analysis of a system consists of two dependent components with degradation facility and load sharing is introduced. The system is considered to be consisted of two components connected in parallel and works dependently where the failure of any component affects the failure of the other one. In addition, it is assumed that there is a common failure between the two components. All failure and repair rates are assumed to be constant follow bivariate exponential distribution. Markov models are used to construct the mathematical model of the system. Analysis of the availability function and steady-state availability of the model is discussed. Reliability and mean time to failure for the system is introduced. A numerical example is given for illustration.},
 year = {2018}
}

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TY  - JOUR
T1  - Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility
AU  - Neama Salah Youssef Temraz
Y1  - 2018/07/13
PY  - 2018
N1  - https://doi.org/10.11648/j.ijssam.20180301.12
DO  - 10.11648/j.ijssam.20180301.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 10
EP  - 15
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20180301.12
AB  - In this paper, analysis of a system consists of two dependent components with degradation facility and load sharing is introduced. The system is considered to be consisted of two components connected in parallel and works dependently where the failure of any component affects the failure of the other one. In addition, it is assumed that there is a common failure between the two components. All failure and repair rates are assumed to be constant follow bivariate exponential distribution. Markov models are used to construct the mathematical model of the system. Analysis of the availability function and steady-state availability of the model is discussed. Reliability and mean time to failure for the system is introduced. A numerical example is given for illustration.
VL  - 3
IS  - 1
ER  -

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Author Information

Neama Salah Youssef Temraz

Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

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APA Style

Neama Salah Youssef Temraz. (2018). Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. International Journal of Systems Science and Applied Mathematics, 3(1), 10-15. https://doi.org/10.11648/j.ijssam.20180301.12

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ACS Style

Neama Salah Youssef Temraz. Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. Int. J. Syst. Sci. Appl. Math. 2018, 3(1), 10-15. doi: 10.11648/j.ijssam.20180301.12

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AMA Style

Neama Salah Youssef Temraz. Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility. Int J Syst Sci Appl Math. 2018;3(1):10-15. doi: 10.11648/j.ijssam.20180301.12

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@article{10.11648/j.ijssam.20180301.12,
  author = {Neama Salah Youssef Temraz},
  title = {Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {3},
  number = {1},
  pages = {10-15},
  doi = {10.11648/j.ijssam.20180301.12},
  url = {https://doi.org/10.11648/j.ijssam.20180301.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20180301.12},
  abstract = {In this paper, analysis of a system consists of two dependent components with degradation facility and load sharing is introduced. The system is considered to be consisted of two components connected in parallel and works dependently where the failure of any component affects the failure of the other one. In addition, it is assumed that there is a common failure between the two components. All failure and repair rates are assumed to be constant follow bivariate exponential distribution. Markov models are used to construct the mathematical model of the system. Analysis of the availability function and steady-state availability of the model is discussed. Reliability and mean time to failure for the system is introduced. A numerical example is given for illustration.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility
AU  - Neama Salah Youssef Temraz
Y1  - 2018/07/13
PY  - 2018
N1  - https://doi.org/10.11648/j.ijssam.20180301.12
DO  - 10.11648/j.ijssam.20180301.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 10
EP  - 15
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20180301.12
AB  - In this paper, analysis of a system consists of two dependent components with degradation facility and load sharing is introduced. The system is considered to be consisted of two components connected in parallel and works dependently where the failure of any component affects the failure of the other one. In addition, it is assumed that there is a common failure between the two components. All failure and repair rates are assumed to be constant follow bivariate exponential distribution. Markov models are used to construct the mathematical model of the system. Analysis of the availability function and steady-state availability of the model is discussed. Reliability and mean time to failure for the system is introduced. A numerical example is given for illustration.
VL  - 3
IS  - 1
ER  -

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