This paper determines the optimum high-trip- level setting of m-out-of-n:G temperature- trip-amplifier systems,used for the protection of nuclear reactors against excess temperatures, which results in the maximum reliability. The bivariate normal distribution is used to simulate the fluctuation of the thermocouple signals and the uncertainties of the trip settings. The thermocouples and the trip amplifiers can fail in two modes of failure: fail-safe and fail-danger. It is shown that by properly selecting the trip levels of the amplifier units the reliability of the protection system is maximized. The optimum trip-level is calculated for various commonly used configurations using a computer algorithm.