6 ◾ System Instantaneous Availability
eigenvalue of system main operators, and it has the corresponding normal eigen-
vector, which proves the system has steady-state normal solution.
Reference [54] discusses the mathematical models for the two same-unit parallel
repairable systems: estimate the resolvent of the main operator, prove the stability of
the main operator, prove the existent uniqueness of nonnegative solutions to paral-
lel repairable systems with strongly continuous operator semigroup, and describe
how the system operators generate a strong, continuous, and normal operator semi-
group. Reference [55] discusses the mathematical models for the dynamic series
repairable systems, proving the existence and uniqueness of nonnegative sol ...