Website is showing the following error:
503 Service Temporarily Unavailable
At the same time the following errors can be found in
[Sat Oct 17 11:50:20.153149 2015] [proxy:error] [pid 12966] AH00959: ap_proxy_connect_backend disabling worker for (127.0.0.1) for 60s
[Sat Oct 17 11:50:20.153161 2015] [proxy_fcgi:error] [pid 12966] [client 10.10.10.10:53377] AH01079: failed to make connection to backend: 127.0.0.1, referer: https://example.com/
Website is using PHP-FPM handler.
PHP-FPM service is stopped.
Check what version of PHP is used by domain in Domains > example.com > PHP Settings.
Start it, for example for PHP 5.6:
# service plesk-php56-fpm start