As a first contact point of a company with customers, call centers are important to keep customers happy and satisfied. There are key performance metrics and other minimum requirements that a Call Center has to meet. In order to improve service quality, performance metrics are monitored by routine daily calls. In this study, the performance metrics of an inbound hospital call center located in Samsun were studied to measure and understand the variability in performance metrics. The control charts were used to detect assignable causes of variability in average speed of answer, abandonment rate and service level so that necessary precautions can be taken to improve process. Since autocorrelation was recognized in data, Autoregressive Integrated Moving Average (ARIMA) model was used to model correlative structure and then control chart were applied to the independent and identically distributed stream of residuals. ARIMA (6,1,1) for all performance metrics was determined as the best time series model to eliminate autocorrelation. The results showed that the call center process was not under statistical control and sources of variability should be investigated and eliminated.