- Journal of Universal Mathematics
- Vol: 2 Issue: 1
- AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL
AN APPLICATION OF PHASE-TYPE DISTRIBUTIONS IN A RELIABILITY SHOCK MODEL
Authors : Mustafa Tekin, Serkan Eryilmaz
Pages : 16-21
Doi:10.33773/jum.506505
View : 16 | Download : 5
Publication Date : 2019-01-30
Article Type : Research
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.Keywords : . Reliability, Shock models, Phase type distribution