What you want for availability from your Linux images is up to you to define in conjunction with your end users' requirements. System availability is not free. It will take effort, and that effort starts with a clear definition of the availability requirements, for example, the various service level agreements with the end users.
Linux as distributed by one of the large distributors with zSeries support is a highly stable operating system benefiting from being both relatively small and having an enthusiastic and skilled group of people dedicated to making it better.
z/VM is a fantastic base on which to run a farm of Linux images. In the first place, you automatically inherit the reliability of the zSeries hardware. z/VM contributes availability tools (such as REXX scripting capabilities) to ensure real time response to events showing up in one or more Linux images. Since z/VM is aware of all the Linux images, it is much easier to build recovery scripts involving related Linux images using z/VM and REXX than it is on most other platforms.
A number of availability management tools from software vendors and the Open Source community also can help you build the level of available Linux servers you need.
At the time of this writing, Linux on the mainframe is not a panacea for all availability problems. However, it is continuously improving and there are many areas where Linux and z/VM are a great pair for delivering the desired levels of availability.