This paper introduces a reliability index that is directly linked to the satisfaction of individual customers with the experienced reliability of supply. The definition of the index is based on the observation that customers are satisfied as long as they have less than 3 interruptions per year, none of which lasts longer than 8 hours. The customer dissatisfaction index (CDI) is defined as the probability that this condition is fulfilled for a given customer. Mathematical expressions are obtained for the CDI; its relation with existing indices is studied; and the results of a case study in a medium-voltage distribution network are presented.