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Point Availability of a Robot with Internal Safety Device

We introduce a robot–safety device system composed of a robot with internal (built–in) safety device. The system is characterized by a safety shut–down rule and by the natural feature of standby. In order to obtain the point availability of the twin–system, we introduce a stochastic process endowed with a probability measure satisfying a (non–standard) integral equation. The explicit solution procedure requires the (new) notion of virtual lifetime - versus - effective lifetime of the robot. The analysis of the long–run availability requires the introduction of a signed measure. As an example, we display a computer–plotted graph of the point availability obtained by inversion of the corresponding Laplace– transform.