1. A remote monitoring system comprising: an equipment monitoring device configured to monitor an operational status of a unit of equipment; and a remote monitoring device configured to receive information relating to the operational status from the equipment monitoring device, the remote monitoring device being provided in a remote location relative to the equipment, the equipment monitoring device including an anomaly detection unit configured to detect an anomaly that occurs in the equipment; an anomaly identifying unit configured to identify the anomaly based on at least one of an anomaly category and an anomaly level which are indicated in a non-reporting condition transmitted from the remote monitoring device, the non-reporting condition being a condition for restricting an anomaly report of the anomaly to the remote monitoring device; and an anomaly reporting unit configured to issue the anomaly report of the anomaly to the remote monitoring based on identification of the anomaly by the anomaly identifying unit, and the remote monitoring device including an anomaly report receiving unit configured to receive the anomaly report, a non-reporting condition generating unit configured to generate and update the non-reporting condition based on the anomaly category and the anomaly level of the anomaly report, and a non-reporting condition transmitting unit configured to transmit the non-reporting condition to the equipment monitoring device.