In this study, we illustrate that the lead time, inventory, and rate of return deviation time series for production processes exhibit similar power-law distribution characteristics by analyzing the actual data. Lead time and inventory are considered to be autonomous distributed systems involving multiple oscillators, and the Kuramoto model is used to represent the synchronization phenomena. As an evidence for the existence of power-law characteristics, we depict that their behaviors demonstrate uctuations and on-off intermittency that can be represented using Langevin dynamics. Finally, we verify that all the three parameters depict power-law distributions using actual data
