Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility
International Journal of Systems Science and Applied Mathematics
Volume 3, Issue 1, March 2018, Pages: 10-15
Received: May 22, 2018;
Accepted: Jun. 14, 2018;
Published: Jul. 13, 2018
Views 1332 Downloads 62
Neama Salah Youssef Temraz, Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
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.
Neama Salah Youssef Temraz,
Availability and Reliability Analysis for Dependent System with Load-Sharing and Degradation Facility, International Journal of Systems Science and Applied Mathematics.
Vol. 3, No. 1,
2018, pp. 10-15.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Barlow R. E. and Prochan F., Statistical Theory of Reliability and Life Testing: Probability Models, Silver Spring, 1981.
Meeker W. Q. and Escobar L. A., Statistical Methods for Reliability Data, Wiley, New York, 1998.
Lawless J. F., Statistical Models and Methods for Lifetime Data, John Wiley & Sons, 1982.
Misra K. B., Handbook of Performability Engineering, Springer-Verlag, London, 2008.
Balakrishnan N. and Lai C. D., Continuous Bivariate Distributions, Springer, New York, 2009.
Marshall A. W. and Olkin I., A Multivariate Exponential Distribution, Journal of American Statistical Association, 62, 30–44, 1967.
Freund J. E., A Bivariate Extension of the Exponential Distribution, Journal of American Statistical Association, 56, 971–977, 1961.
Bailey N. T. J., The Elements of Stochastic Processes, Wiley, New York, 1964.
Huang L. and Xu Q., Lifetime Reliability for Load-Sharing Redundant Systems with Arbitrary Failure Distributions, IEEE Transactions on Reliability, 59, 2, 2010.
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.
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.
Rausand M. and Høyland A., System Reliability Theory: Models, Statistical Methods, and Applications, Wiley, Hoboken, 2004.
Pukite P. and Pukite J., Modeling for Reliability Analysis, IEEE, New York, 1998.
Block H. W. and Basu A. P., A Continuous Bivariate Exponential Extension, Journal of American Statistical Association, 69, 1031–1037, 1974.
Walpole, Ronald E., Myers, and Raymond H., Probability and Statistics for Engineers and Scientists, Macmillan Publishing Company, 1985.