Safety and reliability of safety monitoring system considering complete and transient failure

This paper studies the reliability and safety of the k-out-of-n:G system as well as its optimal structure among the coherent safety monitoring system composed of n identical sensors. Considering the transient failure and complete failure, when the expected loss caused by fail-safe and fail-dangerous is used as the evaluation criteria of safety, the relationship between reliability and safety is expressed by an analytical formula. It is analyzed mathematically that the high reliability cannot completely guaranty its safety. Further, a simple formula to find the optimal k that can minimize I is obtained. The change of the optimal dynamic logic structure as time of the system elapses is argued. Illustrative examples are given.