Reliable design of safety monitoring systems accounting for the uncertainty zone

This paper proposes a probabilistic approach to the design problem of a safety monitoring system considering uncertainty in the monitored object. To reduce the uncertainty, we introduce two types of sensors which have different thresholds, the SP sensor and the FW sensor. The optimal combination problem which we consider here is to determine the optimal combination of the two types of sensors that minimizes the expected value of the loss derived from incorrect ‘system alarm’ or ‘no-alarm’ judgments. We give the analytical solution of the problem, which shows that the optimal combination is determined by only three parameters. Lastly, we show that monitoring with inspection is effective in some cases.