Testing Random Number Generators(RNG)

There are numerous tests of RNGs. Consider that we tested RNG with lots of different seeds and the output is as follows: with certain seeds the RNG passes the test, with other seeds RNG doesn't pass. By passing I mean we 1.fix significance level, 2. find critical value, 3.If the test output is bigger than critical value we reject. Or we may do something like that with p-values. We can fix the seed and for fixed seed take random number sequences from RNG, and we see for some sequences RNG passes the test, for others doesn't pass. So the MAIN question is how check whether RNG good or not, IF some of sequences pass the test, some sequences of THE SAME RNG don't pass? Should I plot the distribution of p-values of test outputs, which we know that is uniformly distributed ?

Thank you very much in advance.