Analytical modeling of series-parallel flow lines

The paper deals with the analytical modeling of series-parallel flow lines, modeled as a continuous time, mixed state Markov process. Machines are assumed to be unreliable with operation dependent failures; failure and repair times are assumed to be independent and exponentially distributed. The methodology to treat such a complex system approximates a parallel-machine stage of the original flow line as an equivalent unreliable machine. Such a technique has been originally proposed by Burman (1995). Nevertheless, the results were not enough accurate in several scenarios. Hence, the work presented in this paper significantly extends the technique proposed by Burman (1995) by describing an iterative procedure for computing the parameters of the equivalent machine with a higher accuracy. Specifically, the solution is here provided for the case where the machines of a certain parallel-machine stage are identical. Once the equivalent machine of each parallel-machine stage has been characterized, the original series- parallel flow line can be analyzed as a simpler serial flow line, extensively discussed in previous literature. Finally, a numerical experimentation is discussed to point out some interesting considerations.