Abstract
This paper studies the reliability and safety of the k-out-of-n: G system as well as its optimal structure. Considering intermittent failure and complete failure, when the expected loss (I) caused by fail-safe (FS) and faildangerous (FD) 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 always guarantee its safety. We discuss how the expected loss, the probability of FS and the probability of FD vary, depending on the reliability of sensor. Further, a simple formula is obtained for the optimal κ that can minimize I. The change of the optimal dynamic logic structure as time of the system elapses is argued. Illustrative examples are given.
