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

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

1. 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.