This paper derives the distribution of the difference between the distances to the first and the second nearest facilities. Facilities are represented as points of regular and random patterns, and distance is measured as Euclidean and rectilinear distances on a continuous plane. Since the difference between the distances is regarded as the additional travel distance of customers when the nearest facility is closed, the distribution of the difference represents the reliability of facility location. The distribution of the difference between the road network distances is also calculated to evaluate the reliability of actual facility location.