Multi-armed-bandits might be useful for determining the effectiveness of multiple variations of a web design simultaneously, when the website in question has high enough traffic that significant results can be achieved quickly.
How it works
The MAB is provided with a list of 'levers' each with their expected conversion rate, which the bandit will discover over repeated attempts.
The "Auto" button on the page starts the test for each module. A random number is generated and compared to the expected conversion rate for the current lever, rewarding the lever or starting the next iteration depending on the value.
A variety of different strategies are present on the page, as are statistical significance calculations and a regret delta for each strategy. The aim is to achieve significance for all levers with minimum regret in the shortest amount of time possible.
If you're looking for a really great set of MAB implementations, this may be a better resource: http://bandit.sourceforge.net/