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The existence of a unique nonnegative time-dependent solution to the repairable system with N failure modes and one standby unit is obtained by using $C_0$-Semigroup theory. The spectral properties and the essential spectrum bound of the stand-by system are discussed by using perturbation method. In the end, we get the desired result that the dynamic(More)
In this paper, we investigate a two-unit standby redundant electronic equipment system under human failure. Using functional analysis and C<sub>0</sub>-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(More)
Based on the theory of the Lagrange's method of multipliers, prove the problems of restricting the part of the best restrictive optimization problem needing to the K-T conditions skillfully. This method can avoid the trivial derivation, rely on the superior difficulty knowledge, it is easy to understand and command.
A repairable system model which is consisted of two redundant robots and one safety unit is established in this paper. We are devoted to discussing the unique existence of the solution and the stability of the studied system by analyzing the spectrum distribution of the system operator in detail. Thus we can obtain stability analysis of the studied(More)
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