Erlang Strength Model for Exponential Effects

• Authors: Gökhan Gökdere , Mehmet Gürcan
• Languages of publication: EN

Abstracts

EN

All technical systems have been designed to perform
their intended tasks in a specific ambient. Some systems
can perform their tasks in a variety of distinctive levels.
A system that can have a finite number of performance
rates is called a multi-state system. Generally multi-state
system is consisted of components that they also can be
multi-state. The performance rates of components constituting
a system can also vary as a result of their deterioration
or in consequence of variable environmental conditions.
Components failures can lead to the degradation
of the entire multi-state system performance. The performance
rates of the components can range from perfect
functioning up to complete failure. The quality of the system
is completely determined by components. In this article,
a possible state for the single component system,
where component is subject to two stresses, is considered
under stress-strength model which makes the component
multi-state. The probabilities of component are studied
when strength of the component is Erlang random variables
and the stresses are independent exponential random
variables. Also, the probabilities of component are
considered when the stresses are dependent exponential
random variables.

Keywords

EN

Reliability; Stress-Strength Model; Multi-StateSystem; Erlang Distribution; Exponential Distribution

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2015
• Volume: 13
• Issue: 1

Dates

accepted

1 - 12 - 2015

received

11 - 11 - 2015

online

31 - 12 - 2015

Contributors

author

Gökhan Gökdere

• Department
  of Statistics, Fırat University, 23119, Elazığ, Turkey

author

Mehmet Gürcan

• Department
  of Statistics, Fırat University, 23119, Elazığ, Turkey

References

• [1] K. E. Ahmed, M. E. Fakry, Z. F. Jaheen. J. Statist. Plann. Infer. 64,297 (1997)
• [2] A. M. Awad, M. K. Gharraf. Commun. Statist. Simul. Computat.15, 189 (1986)
• [3] R. D. Brunelle, K.C. Kapur. IIE Transactions. 31, 1171 (1999)
• [4] S. Chandra, D. B. Owen.Naval Res. Log. Quart. 22, 31 (1975)[Crossref]
• [5] N. Ebrahimi. Naval Res. Log. Quart. 31, 671 (1984)[Crossref]
• [6] E. El-Neweihi, F. Proschan, J. Sethuraman. J.Appl. Probab. 15,675 (1978)[Crossref]
• [7] S. Eryılmaz, J. Multivariate Anal. 99, 1878. (2008)[Crossref]
• [8] S. Eryılmaz. IEEE Trans. Reliab. 59, 644, (2010)
• [9] S. Eryılmaz, F. İşçioğlu. Commun. Statist. Theor. Meth. 40, 547(2011)
• [10] A. İ. Genç. J. Statist. Comput. Simul. 83, 326 (2013)
• [11] I. S. Gradshteyn, I. M. Ryzhik. Table of Integrals, Series andProducts, 6th ed.(Academic Press, California, 2000)
• [12] J. C. Hudson, K. C. Kapur. IIE Transactions. 15, 127 (1983)[Crossref]
• [13] S. Kotz, Y. Lumelskii, M. Pensky. The Stress-Strength Model andits Generalizations. Theory and Applications. (Singapore: WorldScientific, 2003)
• [14] W. Kuo, M. J. Zuo. Optimal Reliability Modeling, Principles andApplications. (New York: John Wiley & Sons, 2003)
• [15] A. W. Marshall, I. Olkin. J. Amer. Statist. Soc. 62, 30 (1966)
• [16] N. A. Mokhlis. Commun. Statist. Theor. Meth, 34, 1643 (2005)
• [17] S. Nadarajah, S. Kotz. Mathematical Problems in Engineering.2006, 1 (2006)
• [18] J. G. Surles, W. J. Padgett. J. Appl. Statist. Sci. 7, 225 (2001)
• [19] M. J. Zuo, Z. Tian, H. Z. Huang. IIE Transactions. 39, 811 (2007)[Crossref]

Identifiers

DOI

10.1515/phys-2015-0057