A node in a cluster fails every $100$ hours while other parts never fail.

$$ On failure of the node the whole system needs to be shutdown, faulty node replaced and

system. This takes $2$ hours.

$$ The application needs to be restarted, which takes $2$ hours.

$$ What is the availability of the cluster $?$

$$ If downtime is $$80$k per hour, the what is the yearly cost $?$