This paper introduces the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the challenge of concept completeness in Concept Bottleneck Models (CBMs). CBMs map black-box visual representations extracted by deep neural networks onto interpretable concepts to enhance decision-making transparency. However, constructing a comprehensive concept bank is challenging, limiting CBM performance. Res-CBM addresses this by using an incremental approach to identify and incorporate missing concepts, improving the performance of any CBM. The Res-CBM consists of two main components: a residual concept bottleneck model that fills in missing concepts using optimizable vectors, and an incremental concept discovery module that converts these vectors into interpretable concepts. The model can be applied to any user-defined concept bank as a post-hoc processing method. Additionally, the paper proposes the Concept Utilization Efficiency (CUE) metric to measure the descriptive efficiency of CBMs. Experiments show that Res-CBM outperforms existing state-of-the-art methods in terms of both accuracy and efficiency, achieving comparable performance to black-box models across multiple datasets. The model is particularly effective in scenarios with limited data, demonstrating superior performance in few-shot learning tasks. The approach also enhances interpretability by translating abstract concepts into human-understandable ones, enabling automatic model debugging. The paper also discusses the importance of concept purity, precision, and completeness in CBMs. It highlights the limitations of existing methods and proposes a solution that addresses these challenges through an incremental approach. The results demonstrate that Res-CBM achieves optimal accuracy with the best concept utilization efficiency, making it a promising approach for improving the interpretability and performance of CBMs.This paper introduces the Incremental Residual Concept Bottleneck Model (Res-CBM) to address the challenge of concept completeness in Concept Bottleneck Models (CBMs). CBMs map black-box visual representations extracted by deep neural networks onto interpretable concepts to enhance decision-making transparency. However, constructing a comprehensive concept bank is challenging, limiting CBM performance. Res-CBM addresses this by using an incremental approach to identify and incorporate missing concepts, improving the performance of any CBM. The Res-CBM consists of two main components: a residual concept bottleneck model that fills in missing concepts using optimizable vectors, and an incremental concept discovery module that converts these vectors into interpretable concepts. The model can be applied to any user-defined concept bank as a post-hoc processing method. Additionally, the paper proposes the Concept Utilization Efficiency (CUE) metric to measure the descriptive efficiency of CBMs. Experiments show that Res-CBM outperforms existing state-of-the-art methods in terms of both accuracy and efficiency, achieving comparable performance to black-box models across multiple datasets. The model is particularly effective in scenarios with limited data, demonstrating superior performance in few-shot learning tasks. The approach also enhances interpretability by translating abstract concepts into human-understandable ones, enabling automatic model debugging. The paper also discusses the importance of concept purity, precision, and completeness in CBMs. It highlights the limitations of existing methods and proposes a solution that addresses these challenges through an incremental approach. The results demonstrate that Res-CBM achieves optimal accuracy with the best concept utilization efficiency, making it a promising approach for improving the interpretability and performance of CBMs.