On the variance of the production output of transfer lines

The variability factor, (i.e., the variance) of the cumulative production, Sigma(t), delivered by a line composed of failure prone machines is studied in the fluid modeling approach, In this context, the evolution of Sigma(t) is described by a stochastic differential equation in which the noise sour ce describes the random failures of the machines. We calculate the fluctuat ions of the production for three different situations, namely for a single non-Markovian machine, for unbuffered networks of Markovian machines and fo r production dipoles composed of two machines separated by one buffer. The dynamics of the production dipole is approached via the introduction of a r andom environment model. Thanks to this new model, we can explicitly take i nto account the buffer induced correlations phenomena which directly influe nce the variability of Sigma(t). The probabilistic properties of the random time needed to complete a batch of fixed size are also explicitly derived.