Finding pattern in binary sequences

I have several binary sequences, and I want to see if it is possible to describe them with a common model.

My first thought is to see if there is a similar pattern in the binary sequences, because if not, there is no point looking for a model to describe them all.

The binary sequences are based on measurements, where a 1 describes an event happening, and a 0 if not. The sampling time of the measurements is the same for all the sequences. At the moment I'm only comparing sequences with five events or more, but I have no idea if this is too few or not. The binary sequences are also very different when it comes to the total length of the sequence.

I'm using Matlab, and I was thinking about using xcorr(), but I'm not sure how to read the results, and how to be able to extract a (possible) pattern.