...I am a bit confused...

Me too, but I may not have had enough coffee, yet.

I don't see that your program's strictly doing what you want it to do, i.e., forming a new order of these strings, since you could be randomly selecting the same element from @X_info multiple times, creating a new set of strings (but perhaps that's what you do want).

However, if your goal is to randomly shuffle the array of strings n times, while maintaining that set of strings, then consider the following:

use warnings;
use strict;
use List::Util qw/shuffle/;

my $runs  = 1000;
my $range = 1553;

my @array = ( 'A' .. 'Z' );
@array = shuffle @array for 1 .. $runs * $range;
print "@array";
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Output:

E I C M P Y D B F Q U J X R V T Z H S N G A O W K L
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Hope this helps!