Process system_add_date_format_type form submissions.
function system_add_date_format_type_form_submit($form, &$form_state) {
$machine_name = trim($form_state['values']['machine_name']);
$format_type = array();
$format_type['title'] = trim($form_state['values']['date_type']);
$format_type['type'] = $machine_name;
$format_type['locked'] = 0;
$format_type['is_new'] = 1;
system_date_format_type_save($format_type);
variable_set('date_format_' . $machine_name, $form_state['values']['date_format']);
drupal_set_message(t('New date type added successfully.'));
$form_state['redirect'] = 'admin/config/regional/date-time';
}