Abstract. In this paper the method, allowing us to determine the database size when correct object has recognition probability higher or equal then given is established. New approach to define the integral probability of correct recognition, when having differential probabilities of correct recognition is proposed. Features of recognition reliability coefficient are considered. We may establish some features, finding the connection between recognition reliability coefficient and probabilities of correct recognition. The local and global transfers are the feature examples of recognition reliability coefficient. We solved some optimization tasks too. So the approach to find the minimal number of spectral components of the Karhunen-Loeve transformation as basic algorithm of recognition system ensuring the admissible value of the probability of existence of the correct object in the confidence interval boundary when solving the clustering object tasks has been developed. We pay much attention to detection problems. As result of our efforts the method allowing us to detect the correct object, replacing on arbitrary positions in confidence interval boundary is developed. Some real numerical results, demonstrating these approaches are given.