Object oriented design is becoming more popular in software development environment and object oriented design metrics are essential parts of software environment. Many new metrics are being proposed for object-oriented systems, but only few have been validated. The primary purpose of this paper is to analytically and empirically validate a set of metrics that can be used to measure the quality of an object-oriented design in terms of the using class inheritance (generalization and specialization). Analytical description for each metric is considered depending on the obtained results from the practical use of these metrics.