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We study the non-equilibrium time evolution of the average transversemagnetisation and end-to-end correlation functions of the random Ising quantumchain. Starting with fully magnetised states, either in the $x$ or $z$direction, we compute numerically the average quantities. They show similarbehaviour to the homogeneous chain, that is an algebraic decay in time toward astationary state. During the time evolution, the spatial correlations, measuredfrom one end to the other of the chain, are building up and finally at longtime they reach a size-dependent constant depending on the distance fromcriticality. Analytical arguments are given which support the numericalresults.Comment: 6 pages, 5 figures, accepted for publication in EPJ

Off equilibrium dynamics in disordered quantum spin chain