A generalized class of correlated run shock models

• Main Authors: Yalcin Femin, Eryilmaz Serkan, Bozbulut Ali Riza
• Format: Article
• Language: English
• Published: De Gruyter 2018-06-01
• Series: Dependence Modeling
• Subjects: compound distributions; dependence; laplace transform; phase-type distributions; shock models
• Online Access: https://doi.org/10.1515/demo-2018-0008

In this paper, a generalized class of run shock models associated with a bivariate sequence {(Xi, Yi)}i≥1 of correlated random variables is defined and studied. For a system that is subject to shocks of random magnitudes X1, X2, ... over time, let the random variables Y1, Y2, ... denote times between arrivals of successive shocks. The lifetime of the system under this class is defined through a compound random variable T = ∑Nt=1 Yt , where N is a stopping time for the sequence {Xi}i≤1 and represents the number of shocks that causes failure of the system. Another random variable of interest is the maximum shock size up to N, i.e. M = max {Xi, 1≤i≤ N}. Distributions of T and M are investigated when N has a phase-type distribution.