This paper studies survival functions and associated failure rates for multicomponent systems which are affected by ageing. The ageing process is modeled by an exponential function with rate affected by the magnitude of stresses from a compound Poisson process shock model. Starting with a one-component shock model, the results are extended to two-components and to general k-components systems. The behaviour of the two-components survival probabilities in subsets of the parameter space is illustrated. The authors fit these models to some medical data concerning appendectomy in Australian twins.