Properties of the System Operator of a Two-Unit Standby Redundant System

In this paper, we investigate a two-unit standby redundant electronic equipment system under human failure. Using functional analysis and C₀-semigroup theory, we first prove the system operator is a densely defined resolvent positive operator. Then, we obtain the ad joint operator of the system operator and its domain and the spectra distribution of the system operator. Furthermore, we prove that 0 is the growth bound of the system operator. Finally, we show that 0 is also the upper spectral bound of the system operator using the concept of co final and relative theory.