Industrial control systems (ICS) are moving from dedicated communications to switched and routed corporate networks, exposing them to the Internet and placing them at risk of cyber-attacks. Existing methods of detecting cyber-attacks, such as intrusion detection systems (IDSs), are commonly implemented in ICS and SCADA networks. However, these devices do not detect more complex threats that manifest themselves gradually over a period of time through a combination of unusual sequencing of activities, such as process-related attacks. During the normal operation of ICSs, ICS devices record device logs, capturing their industrial processes over time. These logs are a rich source of information that should be analysed in order to detect such process-related attacks. In this paper, we present a novel process mining anomaly detection method for identifying anomalous behaviour and cyber-attacks using ICS data logs and the conformance checking analysis technique from the process mining discipline. A conformance checking analysis uses logs captured from production systems with a process model (which captures the expected behaviours of a system) to determine the extent to which real behaviours (captured in the logs) matches the expected behaviours (captured in the process model). The contributions of this paper include an experimentally derived recommendation for logging practices on ICS devices, for the purpose of process mining-based analysis; a formalised approach for pre-processing and transforming device logs from ICS systems into event logs suitable for process mining analysis; guidance on how to create a process model for ICSs and how to apply the created process model through a conformance checking analysis to identify anomalous behaviours. Our anomaly detection method has been successfully applied in detecting ICS cyber-attacks, which the widely used IDS Snort does not detect, using logs derived from industry standard ICS devices.