  The motion-and-time analysis has been a popular research topic in operations
research, especially for analyzing work performances in manufacturing and
service operations. It is regaining attention as continuous improvement tools
for lean manufacturing and smart factory. This paper develops a framework for
data-driven analysis of work motions and studies their correlations to work
speeds or execution rates, using data collected from modern motion sensors. The
past analyses largely relied on manual steps involving time-consuming
stop-watching and video-taping, followed by manual data analysis. While modern
sensing devices have automated the collection of motion data, the motion
analytics that transform the new data into knowledge are largely
underdeveloped. Unsolved technical questions include: How the motion and time
information can be extracted from the motion sensor data, how work motions and
execution rates are statistically modeled and compared, and what are the
statistical correlations of motions to the rates? In this paper, we develop a
novel mathematical framework for motion and time analysis with motion sensor
data, by defining new mathematical representation spaces of human motions and
execution rates and by developing statistical tools on these new spaces. This
methodological research is demonstrated using five use cases applied to
manufacturing motion data.
