An examination of variability and its basic properties for a factory

Variability is a key performance index of a factory. In order to characterize variability of a factory, definitions of bottleneck, utilization, and variability of a single machine are reexamined and clarified. The clarification leads to the introduction of a detail expression for the relationship between cycle time and work-in-progress. In order to quantify variability for factories, the author uses a single machine system to gauge the behaviors, and subsequently derives an explicit expression for the variability, of a simple factory, making use of analogy and the clarified definitions. The obtained results can be applied to many subjects in the field of manufacturing management, such as factory performance analysis, capacity planning, and cycle time reduction. With the derived results, properties of variability for a simple factory in the aspects of utilization versus throughput bottlenecks and nonthroughput bottlenecks, gap effects, and bounds on variability, are examined in detail to shed light on the insights of the stochastic behaviors of a complex factory.