Disruptions and random supplies have been important sources of uncertainty that should be considered in the design and control of supply chains. There have been many real world examples in which a single catastrophic event has simultaneously degraded the capabilities of several suppliers leading...

Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales. The properties as well as the interplay of these two functions are established based upon their homogeneous...

One of the most useful tools for handling multivariate distributions with givenunivariatemarginals is the copula function. Using it, any multivariate distribution function can be represented in a way that emphasizes the separate roles of the marginals and of the dependence structure. Liet...

The extremal dependence of a random vector describes the tail behaviors of joint probabilities of the random vector with respect to that of its margins, and has been often studied by using the tail dependence function of its copula. A tail density approach is introduced in this paper to analyze...

It has been shown that vine copulas constructed from bivariate t copulas can provide good fits to multivariate financial asset return data. However, there might be stronger tail dependence of returns in the joint lower tail of assets than the upper tail. To this end, vine copula models with...

In this paper we study the first passage time for a damage process to exceed a given threshold or for the maximal increment of this process to pass a certain critical value. Conditions under which this first passage time possesses the NBU, the IFRA or the IFR properties are studied. An...

A random vector is said to be of (multivariate) phase-type if it can be represented as the vector of random times until absorptions into various stochastically closed subsets of the finite state space in an absorbing Markov chain. The phase-type distributions are useful since Markovian methods...

This paper is concerned with opportunistic maintenance on a multi-component cumulative damage shock model with stochastically dependent components. A component fails when its cumulative damage exceeds a given threshold, and any such a failure creates a maintenance opportunity, and triggers a...