Consumers are continuously looking for ways of improving their productivity, simplifying their tasks, and streamlining communications both domestically and globally. This has resulted in the need to support different applications and thus the ongoing process of migrating many network services from traditional circuit-switched networks to Internet Protocol (IP) to converged networks. The circuit-switched public switched telephone network (PSTN) was a closed network where cyber-security threats were not a major issue. With the advent of converged networks and IP-based services, service providers, government, and enterprises are concerned about the growing security threat. The new networks and equipment will be subject to many types of threats and their vulnerabilities may expose mission critical applications and infrastructure to risk. Realization of these threats can lead to service outage. Today's communications service provider must decide how to treat the effects of security breaches so as to minimize service downtime. This paper highlights a methodology, with examples to identify the effect of security-related failures and the critical design factors to be considered when modeling service reliability. The ITU-TX.805 standard (now also ISO standard 18028-2), based on the Bell Labs security model, is used to evaluate potential high impact threats and vulnerabilities. The analysis uses the Bell Labs domain technique known as security domain evaluation. One of the critical outputs provides a prioritized understanding of the threats the network is exposed to and the vulnerabilities in the security architecture. The next step in the methodology includes incorporating the threats (vulnerabilities) identified in a reliability model and quantifying the corresponding service degradation. In this paper, these concepts are applied to IP Multimedia Subsystem (IMS)-based VoIP (Voice over IP) networks. Using reliability metrics, our analysis shows that reliability models are optimistic if we do not consider security. We demonstrate how reliability models can be enhanced to take security issues into account and that the X.805 standard can be used to identify the security threats. Finally, the model shows the mitigation in downtime by including intrusion-tolerance features in the product and network design. Consideration of security-caused downtime will lead to increased focus on preventing security vulnerabilities that can lead to service outages and also allow service providers to save on maintenance costs.