How would you do it if you had no computer and had the measured values printed on a sheet of paper?

How would you do it if you had no computer, had the measured values printed on a sheet of paper, but could only ever read one line of paper at a time?

You are allowed to write on additional sheets of paper.

Your code seems to make a range check, whether the value is between 2.5 and 45.5, but only if $N is smaller than 300. If $N is greater than 300, $MIN_TOL and $MAX_TOL seem to be undefined (if you haven't set default values somehwere else in the surrounding code). If not, the value is flagged if it is greater or lower than UNDEF aka 0, which is true for all values except 0.

If you turn on warnings (if you haven't already, do so), perl would warn you about such problems.

my $c = 0;
for (my $i = 1; $i < @data; $i ++) {
    if ($data[$i] eq $data[$i - 1]) {
        if (++$c >= 4) {
            print "Five indentical values in a row, starting at positi
+on ", $i - 4, "\n";
        }
    }
    else {
        $c = 0;
    }
}
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# Stuck value check
for my $index (0 .. $#data - 5) {
    my $first = $data[$index];
    
    next if grep {$first != $_} @data[$index + 1.. $index + 5];

    # Here if a 'stuck' value was found
}
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Note, you should always use strictures (use strict; use warnings;). Use the Perl for loop rather than the C variant - it's a lot clearer and a lot safer.

You iterate over a range in terms of @data, but you never access the array. If @data, @channel and @QV are related data use one data structure to represent them, otherwise there are too many opportunities for the data in the various arrays to get out of sync.

Your range check looks like it should be outside the Station loop.

I am processing environmental variables (hourly measurements) and we declared variables as stuck if we have 5 instances of no-change.

ok then to index the last five elements of an array say @arr up to and including $i, use the array slice

$arr[ ($i - 4) .. $i ]
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update: and to avoid trying to index below 0: and suggesting an inequality function:

my $h = $i - 4;
if ( $h >= 0 ) {
    if (unequal ( $arr[ $h .. $i ] ) {
         # flag stuck value
    }
}

# ...

sub unequal {
    my %v = map { ($_, 1 ); } @_;
    my @v = keys %v;
    return $#v;
}
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One world, one people

I would do it in the simplest way possible:   the first data-structure that comes to mind.   This would be a hashref (of keys...) pointing to an arrayref (of values).

Each time you get a value, you unshift it onto the array.   If the number of entries in the array is now 6, shift off the first one and discard it, then check for identical runs.   (If not, you don’t have enough observations yet.)

The test for runs is also very straightforward:   a while loop.

In short, there is no reason for your coding to be “clever.”   (You are in no danger of running out of microseconds.)   The only thing that matters is that it is clear and maintainable.