Production variability in manufacturing systems: Bernoulli reliability case

The problem of production variability in serial manufacturing lines with un reliable machines is addressed. Bernoulli statistics of machine reliability are assumed. Three problems are considered: the problem of production vari ance, the problem of constant demand satisfaction, and the problem of rando m demand satisfaction generated by another (unreliable) production line. Fo r all three problems, bounds on the respective variability measures are der ived. These bounds show that long lines smooth out the production and reduc e the variability. More precisely, these bounds state that the production v ariability of a line with many machines is smaller than that of a single ma chine system with production volume and reliability characteristics similar to those of the longer line. Since all the variability measures for a sing le machine line can be calculated relatively easily, these bounds provide a nalytical tools for analysis and design of serial production lines from the point of view of the customer demand satisfaction.