Incident-reporting system has been established in various fields, such as airline safety, manufacturing and patient safety etc. A necessity of establishment of incident-reporting system has been conceived, but some problems for an effectiveness of this is still remained. First is about a gap between reporting number and real-occurred number. Some research indicates the gap can exist and be affected by a management styles, such as productivity and safety of work place. This gap is also attributed by a substantial limit of incident system; that is, reporting is autonomous by a reporter and a manager has great difficulty for clarifying an appropriateness of reporting. Second is evaluating difficulty of an effectiveness of the reporting system. As already-known, a change of reporting number, which is an only visible value for a manager of an organization, is not necessarily reflected in actual change of frequency of occurrence. It is difficult to evaluate the effectiveness only with the number of reporting. We then need to attain some quantitative index reflecting number of occurrence, to evaluate the effectiveness in quantity, which all person can conceive rationally. In this paper we propose a quantitative index of enthusiasm of reporting, which is a main part of Reason's organizational safety culture, to evaluate this effectiveness. We observed the relationship between our proposed index and a frequency of fatal incident in one hospital organization. The result showed negative correlation in two factors, as we predicted. Then this value can be regarded as a quantitative index of enthusiasm of reporting, based on experienced relation to the frequency of fatal incident.