I have six strings of data; each string consists of bits obtained from a device run over the same 12 hour period (the six experiments were run on six devices simultaneously). Most of the data are 0's, but occasionally (about 5% of the time) there's a 1. I want to test the hypothesis that the strings are synchronized, such that if a "1" occurs in one string, it's more likely to occur in the same position in the other strings (or at least close - within a couple of positions). Basically the idea is to test whether the positions of 1's in the strings are completely independent of each other, or if there's a significant correlation among them such that a "1" in one string is indicative of a higher probability of a 1 in the other strings. What statistical test should I use?