  Availability analysis is used to assess the possible failures and their
restoration process for a given system. This analysis involves the calculation
of instantaneous and steady-state availabilities of the individual system
components and the usage of this information along with the commonly used
availability modeling techniques, such as Availability Block Diagrams (ABD) and
Fault Trees (FTs) to determine the system-level availability. Traditionally,
availability analyses are conducted using paper-and-pencil methods and
simulation tools but they cannot ascertain absolute correctness due to their
inaccuracy limitations. As a complementary approach, we propose to use the
higher-order-logic theorem prover HOL4 to conduct the availability analysis of
safety-critical systems. For this purpose, we present a higher-order-logic
formalization of instantaneous and steady-state availability, ABD
configurations and generic unavailability FT gates. For illustration purposes,
these formalizations are utilized to conduct formal availability analysis of a
satellite solar array, which is used as the main source of power for the Dong
Fang Hong-3 (DFH-3) satellite.
