Variability and the fundamental properties of production lines

The concept of variability has been commonly used in practice and it is an important performance index of manufacturing systems. In this study, the definition of system variability is given through the insight of Kingman's approximation. The explicit expression for the variability of a production line is derived based on intrinsic ratios and contribution factors. With the derived results, properties of variability for a production line in terms of job arrival rate, service rate and bounds on variability are examined. Simulation results are given to validate the derived properties. The result can be used to guide the design and operations of manufacturing systems.