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

#### Mustafa TEKİN [1] , Serkan ERYILMAZ [2]

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.

. Reliability, Shock models, Phase type distribution
• 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.
Primary Language en Mathematics Research Article Author: Mustafa TEKİN (Primary Author)Institution: Gazı UniversityCountry: Turkey Author: Serkan ERYILMAZInstitution: ATILIM UNIVERSITYCountry: Turkey Application Date : January 2, 2019 Acceptance Date : January 26, 2019 Publication Date : January 30, 2019
 Bibtex @research article { jum506505, journal = {Journal of Universal Mathematics}, issn = {2618-5660}, eissn = {2618-5660}, address = {editorinchief@junimath.com}, publisher = {Gökhan ÇUVALCIOĞLU}, year = {2019}, volume = {2}, pages = {16 - 21}, doi = {10.33773/jum.506505}, title = {AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL}, key = {cite}, author = {Tekin, Mustafa and Eryılmaz, Serkan} } 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 . DOI: 10.33773/jum.506505 MLA Tekin, M , Eryılmaz, S . "AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL" . Journal of Universal Mathematics 2 (2019 ): 16-21 Chicago Tekin, M , Eryılmaz, S . "AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL". Journal of Universal Mathematics 2 (2019 ): 16-21 RIS TY - JOUR T1 - AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL AU - Mustafa Tekin , Serkan Eryılmaz Y1 - 2019 PY - 2019 N1 - doi: 10.33773/jum.506505 DO - 10.33773/jum.506505 T2 - Journal of Universal Mathematics JF - Journal JO - JOR SP - 16 EP - 21 VL - 2 IS - 1 SN - 2618-5660-2618-5660 M3 - doi: 10.33773/jum.506505 UR - https://doi.org/10.33773/jum.506505 Y2 - 2019 ER - EndNote %0 Journal of Universal Mathematics AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL %A Mustafa Tekin , Serkan Eryılmaz %T AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL %D 2019 %J Journal of Universal Mathematics %P 2618-5660-2618-5660 %V 2 %N 1 %R doi: 10.33773/jum.506505 %U 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 AMA Tekin M , Eryılmaz S . AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. JUM. 2019; 2(1): 16-21. Vancouver Tekin M , Eryılmaz S . AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL. Journal of Universal Mathematics. 2019; 2(1): 16-21. IEEE M. Tekin and S. Eryılmaz , "AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL", Journal of Universal Mathematics, vol. 2, no. 1, pp. 16-21, Jan. 2019, doi:10.33773/jum.506505

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