I can put an upper bound on the strength: an attacker who can observe a number of consecutive outputs equal to the sum of the lengths of the individual arrays can deduce the values of the arrays and all subsequent output.
Consider the simple case of three arrays, with lengths 2, 3, and 5: the first ten values (the
a variables), and the hidden values that generate them (the
x variables), are shown below. Each column is the three hidden values that are xored to produce the visible output.
x1 x2 x1 x2 x1 x2 x1 x2 x1 x2
x3 x4 x5 x3 x4 x5 x3 x4 x5 x3
x6 x7 x8 x9 x0 x6 x7 x8 x9 x0
a0 a1 a2 a3 a4 a5 a6 a7 a8 a9
If you turn it sideways, this looks an awful lot like a system of ten equations in ten unknowns -- the sort of thing people learn to solve in introductory algebra. Although the cycle length is 30, only 10 consecutive values are needed to completely characterize the generator and predict the next value.
As the number of arrays grows, so does the disparity between cycle length and ease of breaking it: ten arrays of length 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 gives a cycle length of 6,469,693,230, but only requires 129 values to break.
It may be possible for an attacker who already knows the contents of the arrays to break security with fewer values, but I'm not sure how it would be done.