The rapid development of robust, reliable, and reduced-order process-structure evolution linkages that take into account hierarchical structure are essential to expedite the development and manufacturing of new materials. Towards this end, this paper lays a theoretical framework that injects the established time series analysis into the recently developed materials knowledge systems (MKS) framework. This new framework is first presented and then demonstrated on an ensemble dataset obtained using small-angle X-ray scattering on semi-crystalline linear low density polyethylene films from a synchrotron X-ray scattering experiment.