Production variability in manufacturing systems: Performance bounds and monotonicity properties

Abstract

Production variability in serial manufacturing lines with unreliable machines and finite buffers is addressed. Bernoulli statistics of machines breakdowns are assumed. Two problems are considered: the problem of production variance and the problem of constant demand satisfaction. For both problems, bounds on the respective variability measures are derived. Counter-intuitively, these bounds show that the production variability of a line with many machines is smaller than that of a single machine having the production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a single machine can be calculated relatively easily, these bounds provide analytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction. In addition, monotonicity properties of the variability measures with respect to machines and buffers parameters are investigated and, again counter-intuitively, it is shown that improving machines and/or increasing buffers may not lead improved production variability. A sufficient condition under which this improvement does, in fact, take place is derived.