I am trying to discover the best way to show management how automation will result in increased quality. I have only used automation on our application with a few simple test cases. I don't know how I can show numbers. Any help would greatly be appreciated.
It would be almost impossible to show numbers on such a small sample. What you need to do is put together a scope document which would show that as automation comes up to speed, and it is usually a very slow progress, it will free up manual testers from running the regression tests so they can focus on increasing the manual test coverage. Most likely it will not replace any manual testers so don't brag about that. That could cause hostility from the manual side and you need their approval of this also. But by broadening the test coverage and writing more detailed scripts permitting them to drill down to more hard to find defects, the overall end product is better quality. Also point out that in order to not waste time, though I'm sure you are skilled, you need resource by-in. Get trained, certified contractor to get you set up and running and also to provide training so that you and any other automation person can get off on the right foot. Automation is great!~ But it's Automation, not Automagic!
Success is the ability to go from one failure to another with no loss of enthusiasm.
~ Winston Churchill ~