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AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL

Year 2019, , 16 - 21, 30.01.2019
https://doi.org/10.33773/jum.506505

Abstract

Phase-type distributions have been found to be very useful in reliability,
queueing theory, and some other operational research applications. In this
work, we de_ne a new mixed shock model and study lifetime properties of the
corresponding system using phase-type distributions. The system under concern
fails upon the occurrence of k consecutive shocks of size at least d1 or a
single large shock of size at least d2, d1 < d2. In particular, using
closure properties of phase-type distributions, we obtain survival function and
mean time to failure of the system. Optimal replacement time is also studied. 

References

  • Neuts, M. F., Meier, K. S., On the use of phase type distributions in reliability modelling of systems with two components. OR Spektrum, 2(4), 227-234, 1981Ahmad R., Kamarudin S., An overview of time-based and condition-based maintenance in industrial application, Computers & Industrial Engineering 63(1), 135-149, 2012 Gut, A. Mixed shock models, Bernoulli 7(3), 541-555, 2001. He, Q. M., Fundamentals of Matrix-Analytic Methods. NewYork: Springer, 22-43, 2014 Eryilmaz, S., Computing optimal replacement time and mean residual life in reliability shock models Computers & Industrial Engineering, 103, 40-45, 2017. Eryilmaz, S. and Tekin, M., Reliability evaluation of a system under a mixed shock model, 2018, submitted for publication.
Year 2019, , 16 - 21, 30.01.2019
https://doi.org/10.33773/jum.506505

Abstract

References

  • Neuts, M. F., Meier, K. S., On the use of phase type distributions in reliability modelling of systems with two components. OR Spektrum, 2(4), 227-234, 1981Ahmad R., Kamarudin S., An overview of time-based and condition-based maintenance in industrial application, Computers & Industrial Engineering 63(1), 135-149, 2012 Gut, A. Mixed shock models, Bernoulli 7(3), 541-555, 2001. He, Q. M., Fundamentals of Matrix-Analytic Methods. NewYork: Springer, 22-43, 2014 Eryilmaz, S., Computing optimal replacement time and mean residual life in reliability shock models Computers & Industrial Engineering, 103, 40-45, 2017. Eryilmaz, S. and Tekin, M., Reliability evaluation of a system under a mixed shock model, 2018, submitted for publication.
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Mustafa Tekin

Serkan Eryılmaz

Publication Date January 30, 2019
Submission Date January 2, 2019
Acceptance Date January 26, 2019
Published in Issue Year 2019

Cite

APA Tekin, M., & Eryılmaz, S. (2019). AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. Journal of Universal Mathematics, 2(1), 16-21. https://doi.org/10.33773/jum.506505
AMA Tekin M, Eryılmaz S. AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. JUM. January 2019;2(1):16-21. doi:10.33773/jum.506505
Chicago Tekin, Mustafa, and Serkan Eryılmaz. “AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL”. Journal of Universal Mathematics 2, no. 1 (January 2019): 16-21. https://doi.org/10.33773/jum.506505.
EndNote Tekin M, Eryılmaz S (January 1, 2019) AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. Journal of Universal Mathematics 2 1 16–21.
IEEE M. Tekin and S. Eryılmaz, “AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL”, JUM, vol. 2, no. 1, pp. 16–21, 2019, doi: 10.33773/jum.506505.
ISNAD Tekin, Mustafa - Eryılmaz, Serkan. “AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL”. Journal of Universal Mathematics 2/1 (January 2019), 16-21. https://doi.org/10.33773/jum.506505.
JAMA Tekin M, Eryılmaz S. AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. JUM. 2019;2:16–21.
MLA Tekin, Mustafa and Serkan Eryılmaz. “AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL”. Journal of Universal Mathematics, vol. 2, no. 1, 2019, pp. 16-21, doi:10.33773/jum.506505.
Vancouver Tekin M, Eryılmaz S. AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. JUM. 2019;2(1):16-21.