Abstract
In this paper we study bivariate life distribution functions for the two units subject to sequences of shocks. The following three stochastically independent shock processes are considered: a shock from source 1 is to the unit 1 only, a shock from source 2 is to the unit 2 only and a shock from source 3 is to both units simultaneously. A shock from source i (i=1, 2, 3) occurs randomly in time as events in a Poisson process. If unit i does not fail till it receives ki shocks (i=1, 2), bivariate life distribution functions for two units is called bivariate Erlang distribution functions (BVEr). Throughout the paper monotonic dependency and some properties of BVEr are discussed. It is shown that BVEr has not bivariate increasing failure rate property.
