Contact centers play a critical role in service businesses by acting as the interface between customers and organizations. They are strategic tools to establish a relationship with customers to promote customer satisfaction, which can lead to an increase in customer loyalty and sales. One important factor impacting customer satisfaction is service reliability, which should be constantly monitored to enhance customer satisfaction. This paper uses a systems thinking approach to investigate contact centers from a systems perspective. We aim to provide a holistic view of the customer support process to help decision makers infer transformations in the system. We present an architecture of the contact center operations management system incorporating concepts of systems engineering, and describe its components and functions. The systems perspective to contact center processes facilitates developing a customer service reliability model. Since the reliability metric takes into account the fundamentals of the contact center processes and key input data, the modeling approach can dynamically adapt to changes in the contact center processes and data. The developed system architecture and reliability metric are general and adaptable to be expanded to other domains. An empirical analysis using data from a major insurance company is provided to illustrate the applicability of the system design, reliability, and performance control using a control chart.