A multi-state model of the aging process of cyber-physical systems

Cyber-Physical Systems (CPSs) are systems with tight integration and dependence between software and hardware parts, typically used as control systems and supervised by human operators. In this paper, we propose a multi-state model (commonly used to model the hardware degradation) to describe the aging of the cyber part of a CPS, where memory leakage is considered as the degradation process that leads to a service rate decrease, resulting in data jamming in the mission queue which, in turns, increases the memory request. The CPS is blocked and significantly increases the control delay when the amount of memory available cannot satisfy the demand of the mission queue. With control delay, the CPS may fail to control the system during transients: as an example, a typical Nuclear Power Plant (NPP) control rod system is taken as the CPS and its cyber degradation process modelled with the proposed multi-state degradation model. The unreliability of control rod system is quantified with respect to a transient of power step change, considering cyber degradation and hardware stochastic failure.