In this paper we introduce a quality model that reflects fabrication process quality, design delay margin, and test timing accuracy. The model provides a measure that can predict the level of chip defects that cause delay failure, including marginal delay. We can therefore use the model to make test vectors that are effective in terms of both testing cost and chip quality. The results of experiments using ISCAS89 benchmark data and some large industrial design data reflect various characteristics of our statistical delay quality model.