In this paper we develop a variant of a previously proposed method (the regenerative randomization method) for the transient analysis of dependability performability models. The variant is obtained by developing a closed-form expression for the solution of the truncated transformed model obtained in regenerative randomization and using a Laplace transform inversion algorithm. Using models of moderate size of a 5-level RAID architecture we compare the new variant with the original randomization method, with randomization with steady-state detection for irreducible models, and with the standard randomization method for transient models (models with absorbing states).