In this paper, tritium analyses in titanium films has been carried out by β-decay induced X-ray spectroscopy (BIXS), based on Monte Carlo simulations and the Tikhonov regularization. In our analysis, for the first time the internal bremsstrahlung of tritium β-decay has been taken into account in the BIXS method. Meanwhile, parallel computation using the Monte Carlo code PENELOPE has been realized within the frame of a message passing interface. The tritium depth distributions, surface homogeneity and the total tritium content of the analyzed samples have been obtained. The total tritium contents obtained by the present BIXS method are found to be in good agreement with those obtained by the PVT method.