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

Year 2019, Volume: 2 Issue: 1, 16 - 21, 30.01.2019

Mustafa Tekin Serkan Eryılmaz

https://doi.org/10.33773/jum.506505

Cited By: 2

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

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.