Consider a system that consists of several components. Shocks arrive according to a counting process (which may be non-homogeneous and with correlated interarrival times) and each shock may simultaneously destroy a subset of the components. Shock models of this type arise naturally in...

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...

The tail dependence indexes of a multivariate distribution describe the amount of dependence in the upper right tail or lower left tail of the distribution and can be used to analyse the dependence among extremal random events. This paper examines the tail dependence of multivariate...

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...

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...

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...

In risk management, ignoring the dependence among various types of claims often results in over-estimating or under-estimating the ruin probabilities of a portfolio. This paper focuses on three commonly used ruin probabilities in multivariate compound risk models, and using the comparison...

The orthant tail dependence describes the relative deviation of upper- (or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach,...

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...