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Cyber-attack detection is used to identify cyber-attacks while they are acting on a computer and network system to compromise the security (e.g., availability, integrity, and confidentiality) of the system. This paper presents a cyber-attack detection technique through anomaly-detection, and discusses the robustness of the modeling technique employed. In this technique, a Markov-chain model represents a profile of computer-event transitions in a normal/usual operating condition of a computer and network system (a norm profile). The Markov-chain model of the norm profile is generated from historic data of the system's normal activities. The observed activities of the system are analyzed to infer the probability that the Markov-chain model of the norm profile supports the observed activities. The lower probability the observed activities receive from the Markov-chain model of the norm profile, the more likely the observed activities are anomalies resulting from cyber-attacks, and vice versa. This paper presents the learning and inference algorithms of this anomaly-detection technique based on the Markov-chain model of a norm profile, and examines its performance using the audit data of UNIX-based host machines with the Solaris operating system. The robustness of the Markov-chain model for cyber-attack detection is presented through discussions & applications. To apply the Markov-chain technique and other stochastic process techniques to model the sequential ordering of events, the quality of activity-data plays an important role in the performance of intrusion detection. The Markov-chain technique is not robust to noise in the data (the mixture level of normal activities and intrusive activities). The Markov-chain technique produces desirable performance only at a low noise level. This study also shows that the performance of the Markov-chain techniques is not always robust to the window size: as the window size increases, the amount of noise in the window also generally increases. Overall, this study provides some support for the idea that the Markov-chain technique might not be as robust as the other intrusion-detection methods such as the chi-square distance test technique , although it can produce better performance than the chi-square distance test techn- ique when the noise level of the data is low, such as the Mill & Pascal data in this study.