## 5 Conclusions  
This paper proposes a systematic approach by integrating feature models with feature specification descriptions. Feature model construction, evolution, and specification consistency checks are facilitated by each other to obtain internally consistent product family models which contain product family feature models and corresponding formal specifications. In terms of internal validity [38], it will be difficult to avoid inconsistencies in the feature model when building a specific product after only one round of specification of the initial feature model without using our approach. After using our method, the consistency problems of variables, feature scenarios, and feature paths are excluded, and the quality of the product family model is improved. We illustrate with a few simple examples that our approach applies to product line engineering in different domains. In subsequent work, we will evaluate the computational efficiency of our approach and its applicability to large product line engineering by analyzing a large product line. We provide a support tool that allows users to select suitable templates to build and evolve feature models without knowledge of PFA, then describe the internal structure of each feature with formal specifications based on the generated feature models, and finally perform consistency checks on the formal specification descriptions. In addition, we provide advice to solve inconsistencies by corresponding actions for the checked inconsistencies to facilitate feature model evolution and finally obtain internally consistent product family models. After four examples of practice, our approach proved to be effective in improving the consistency of the product family model. Using the approach proposed in this paper helps to obtain internally consistent product family models. The product family models obtained according to the method include feature models with feature specifications, and product-specific model specifications can be derived from the feature models and the formal language. Our approach has some limitations identified by tool implementation and experimental analysis. First, with our approach, in order to improve efficiency and industrial usability, the tool only tests for variable consistency and path range consistency in the formal description, and ignores the presence of other conditions in the postcondition that do not meet the test specification, which may lead to some existing problems that are not detected. Second, although our tool sets the input content and formatting requirements for the formal language, it still requires a certain level of knowledge of the SOFL formal language. In future work, we will further expand the range of variables that can be supported, and \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Product** & **Initial** & **Final** & **Inconsistency** & **Evolution** \\  & & & **Number** & **Number** \\ \hline RMS & 7 & 12 & 5 & 3 \\ ACCS & 17 & 23 & 8 & 4 \\ AMS & 14 & 17 & 2 & 2 \\ MPP & 13 & 15 & 3 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Product family evolutionary process. \begin{table}
\begin{tabular}{c c} \hline \hline
**Product** & **PFA Expressions** \\ \hline RMS & MM\(\cdot(\text{WS-Safe-DTW-opt[SD]})\cdot\text{SGM-opt[DAM]}\cdot(\text{opt[Message]-opt[RO]})\) \\ ACCS & \((\text{Modbus}+\text{CAN})\cdot(\text{R22}+\text{R410})\cdot(\text{HC}+\text{ HP})\cdot(\text{opt[TC]}+\text{opt[PC]})\cdot(\text{Semi}+\text{ED})\cdot(\text{FOT}+ \text{DT})\cdot(\text{opt}[\text{PEV}]+\text{opt[TEV]})\cdot(\text{CW-opt[A/DA]}\) \\ AMS & Register\(\cdot(\text{TOL-OSL-RL})\cdot\text{DM-OCOC}\cdot(\text{CC}+\text{US}+\text{BV})\cdot opt[\text{OOMP}]\) \\ MPP & \((\text{Mess-Tele-opt[Net]})\cdot opt[\text{GPS}]\cdot(\text{Basic-Color- HighRes})\cdot(\text{opt[Camera]}+\text{opt[MP3]}+\text{opt[MP4]}+\text{opt[(Camera-MP3)]})+\text{opt[(Camera-MP4)]}+\text{opt[(MP3-MP4)]}+\text{opt[(Camera-MP3-MP4)]})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Example system product family PFA expressions.