We consider the robot-safety device system as described in: Vanderperre and Makhanov, International Journal of Reliability, Quality and Safety Engineering 7 (2000) 169-175. The engineering system is characterized by the natural feature of cold standby and by a possible risky state. Apart from some tangible results obtained in the previous Literature, we introduce a risk function associated with the risky state of the robot. The risk function is determined by a coupled pair of convolution-type integral equations. In order to decide whether the risky state is admissible or reprehensible, we also introduce a suitable risk-criterion involving the supremum norm. We demonstrate that the criterion is always satisfied in the particular but important case of "fast" repair. Finally, we propose a numerical procedure to solve the system of integral equations and we calculate the underlying risk function.