Title :
On the variance of the production output of transfer lines
Author :
Ciprut, Philippe ; Hongler, Max-Olivier ; Salama, Yves
Author_Institution :
Ecole Polytech. Fed. de Lausanne, Switzerland
fDate :
2/1/1999 12:00:00 AM
Abstract :
The variability factor, (i.e., the variance) of the cumulative production, Σ(t), delivered by a line composed of failure prone machines is studied in the fluid modeling approach. In this context, the evolution of Σ(t) is described by a stochastic differential equation in which the noise source describes the random failures of the machines. We calculate the fluctuations of the production for three different situations, namely for a single nonMarkovian machine, for unbuffered networks of Markovian machines and for production dipoles composed of two machines separated by one buffer. The dynamics of the production dipole is approached via the introduction of a random environment model. Thanks to this new model, we can explicitly take into account the buffer induced correlations phenomena which directly influence the variability of Σ(t). The probabilistic properties of the random time needed to complete a batch of fixed size are also explicitly derived
Keywords :
batch processing (industrial); correlation theory; differential equations; probability; production control; reliability theory; stochastic processes; Markovian machines; buffer induced correlations; cumulative production; failure prone machines; fluid modeling approach; noise source; probabilistic properties; production dipoles; production fluctuations; production output variance; random failures; single nonMarkovian machine; stochastic differential equation; transfer lines; unbuffered networks; variability factor; Differential equations; Flow production systems; Fluctuations; Fluid dynamics; Fluid flow control; Frequency; Stochastic resonance; Throughput; Time measurement;
Journal_Title :
Robotics and Automation, IEEE Transactions on