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Risk-Criterion for a Single Robot with External Safety Device

We introduce a robot-safety device system characterized by cold stand-by and by an admissible risky state. The system is attended by a single repairman and all the underlying repair time distributions are arbitrary. We obtain an explicit formula for the point availability of the robot-safety device system via an integral equation of the convolution-type. In order to decide whether the risky state is admissible, we introduce a risk-criterion based on the notion of rare events. The criterion is always satisfied in the case of fast repair. As an example, we consider the case of Coxian repair and we display a computer-plotted graph of the point availability obtained by numerical inversion of the corresponding Laplace-transform.