The lifelengths of components of a system are usually dependent due to the common random production and operating environments. In this paper, we introduce a multi-variate pure jump Markov process to describe a large class of damage processes on various system components driven by common environmental shocks, and establish some dependence properties (association) for such a process and its multivariate increment process. These strong association properties describe both spatial dependence and temporal dependence of a multivariate pure jump process, and also provide a vehicle to derive some structural properties of component lifelengths of the systems operating in such an environment. Some bounds for the joint survival functions of component lifelengths are also obtained.
