Let \(T_ i\) denote the lifelength of component i \((i=1,...,N)\) of a parallel system. Let be given a stochastic process \(Y=\{Y_ t\), \(t\geq 0\}\) which is exogeneous to the failure mechanism and has cadlag trajectories. The lifelengths \(T_ i\) are independent and \[ \lim_{\tau \to 0}(1/\tau)P[t<T_ i\leq t+\tau | T_ i>t,Y]=\xi_ i(t,Y_ t),\quad i=1,...,N, \] where each \(\xi_ i(t,y)\) is a positive continuous function of \(t\in {\mathbb{R}}_+\) and \(y\in {\mathbb{R}}\). If the process Y is associated, then the lifelengths \(T_ i\) as well as the risks \(Q_ i(t_ i)=\int^{t_ i}_{0}\xi_ i(u,Y_ u)du\), \(t_ i\geq 0\), are associated for \(i=1,...,N\).