Not disagreeing, just commenting that I would have assumed that taking the entire system offline for a reboot on a weekly basis would be untenable from a business perspective. It seems at odds with the concept of all the redundancy built into mainframes to ensure high availability and uptimes. Given that many mainframe-based systems (e.g. airline reservations) generally need to be available 24/7/365, I would have assumed that while one part of the system is being rebooted, others are still available so the overall application can continue to run uninterrupted.
That way you don't have to try and organize downtime if maintenance is required, you know every sunday morning is available when needed.