A system of n components is here considered, with component deterioration modeled by non decreasing time-scaled Lévy processes. When a component fails, a sudden change in the time-scaling functions of the surviving components is induced, which makes the components stochastically dependent. We compute the reliability function of coherent systems under this new dependence model. We next study the distribution of the ordered failure times, and establish some positive dependence properties. We also provide stochastic comparison results in the usual multivariate stochastic order between failure times of two dependence models with different parameters. Finally, some numerical experiments illustrate the theoretical results.