In this paper, we consider the procedure to estimate the various effects of the design factors in the two-stage series lines in which the first stage has an arbitrary service time. First, the system states are represented by the imbedded Markov chain and the steady state probabilities are solved by the Laplace transform with respect to the arbitrary service time distribution. Next, the efficiency, the idling time distribution, the blocking time distribution and the number of in-process works distribution are considered from the system states. Moreover the relations between the dual models are discussed.