Use some kind of configuration -- hash, external files, __DATA__, etc -- to associate processes to a server ...

# Untested, incomplete code.

my %map =
  ( 'host-p' => [qw[ cron apache ]]
  , 'host-q' => [qw[ ntpd ]]
  );

for my $host ( sort keys %map )
{
  #  Log on $host at this point.

  #  Check processes.
  foreach my $proc ( @{ $map{ $host } } )
  {
    printf qq[%s: %3s running]
      , $proc
      , check_proc( $proc ) ? '' : 'not' ;
  }

  #  Log off.
}

sub check_proc
{
  my ( $proc ) = @_;

  my $ps = make_ps( $proc );
  my $res = qx[ $ps ];
  # Check $? for cause of failure if you care.

  return
    defined $res && $res =~ m{ \b psname = $proc \b }x;
}

sub make_ps
{
  return sprintf q[ps -ef | grep psname=%s] , $_[0] ;
}
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Your process checking looks too complicated; there might be OS specific commands/options that won't require filtering of ps run itself. Perhaps some native Perl module may be in existence for the purpose.