Because of their automated processing capabilities, industrial control systems (ICSs) currently play a crucial role in plant operations. It was not long before ICS had been completely insulated from the Internet. However, because of the improved reliability of ICS devices and systems, we could find only a few plants that did not use ICS in conjunction with the Internet. As a result, the extended accessibility of almost every ICS component makes such systems vulnerable to cyber-attacks. Because of this, intrusion detection systems, which monitor ICS network traffic and detect suspicious activities within the components themselves, are extremely important. Previous studies argued that packet intervals could ideally be regarded as indicators of the hazardous status of ICSs against hacking activities, and proposed intrusion detection methodologies relying solely on packet intervals. However, these methodologies with supervised machine-learning have inevitably been compromised by cyber-attacks whose characteristics are different than those of the training dataset. We hypothesize that packet intervals in an ICS network used for automated industrial processes, which are forced to produce a certain type of periodicity, reflect a particular type of packet interval patterns. In other words, certain anomalous behaviors never fail to interfere with this pattern. This paper proposes an intrusion detection method using a singular spectrum analysis to monitor time series packets. We evaluated our proposed method on our cybersecurity testbed using penetration tests. The results verified the validity of our system realized in the packet interval periodicity. Furthermore, we examined the optimum parameter set for the singular spectrum analysis in the proposed method. From this experiment, we successfully designated criteria for the parameter-set based on the period of the packet intervals during normal operations. The proposed method successfully detected all three types of attacks within 4 sec, without producing a false alert during normal operations.