This research establishes a multidimensional capacity indicator that allows to evaluate the sigma level of the service dimensions in a call centre of a telephone company. This study is based on the concepts of statistical control, specifically multidimensional capacity, service quality and sigma level associated with the Six Sigma metrics. As a result, a method to measure service is proposed, through the proposal of a multidimensional indicator of capacity for the utility under study, that showed a value of 0.1534, this is distant from the ideal minimum value that is the unit; therefore, the areas of application of protocols and escalation of the office service were identified, the causes of the decrease of the indicator. The proposed multidimensional capacity indicator is rigorous to evaluate the performance; this implies that using this indicator in the Six Sigma methodology is considerably more rigorous than the traditional Six Sigma evaluations.