Journal article

On the variance of the production output of transfer lines

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 non-Markovian machine, for unbuffered networks of Markovian machines and for production dipoles composed of two machines separated by one buffer. The dynamics of the production dipoleis approached via the introduction of a random environment mode. Thanks to this new mode, 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: Alternating renewal processes ; Batch completion time ; Fluid modeling ; Production dipole ; Production flows ; Differential equations ; Markov processes ; Mathematical models ; Production control


    Ecole Polytechnique Fédérale de Lausanne, Switzerland

    Cited By (since 1996): 14

    Export Date: 6 December 2012

    Source: Scopus


    Language of Original Document: English

    Correspondence Address: Ecole Polytechnique Fédérale de LausanneSwitzerland

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