Secondary vocational education (SVE) plays a crucial role in national economic development, yet faces challenges such as skill mismatches between the supply of graduates and industry demands. This study addresses the lack of quantitative research on the interaction between SVS program structures and industries. The research questions are: 1) What coupling coordination relationship exists? 2) How can this relationship be measured? 3) What factors affect this relationship? The study uses a coupling and coordination perspective to build a conceptual framework and a quantitative computation model, employing grey relational analysis to investigate influencing factors using data from Tianjin, China. Effective SVE programs are vital for a dynamic labor market, ensuring graduates' smooth entry into employment and reducing skill mismatches that hinder economic growth.

Existing research explores the vocational education-industry relationship using various approaches. Tran (2021) used a dynamic network DEA model to analyze Austria's vocational education, highlighting the importance of interaction between providers, students, and employers. Olazaran et al. (2019) identified factors influencing school-firm relationships, such as company size and industry type. Cui and Li (2021) examined the link between culture and art talent training and regional cultural industry development. Studies also emphasize feedback mechanisms (Cedefop, 2013) and the influence of industry and occupation structures on educational attainment (Raffe and Willms, 1989). Despite the increasing focus on skills development, skill mismatches persist (Cedefop, 2015), underscoring the need for closer links between vocational education and industry. Previous work using conjugation theory (Ren et al., 2021) has revealed a generally good but structurally insufficient relationship between vocational education and production, highlighting the need for stronger coupling and coordination.

The study utilizes a coupling and coordination framework to analyze the relationship between SVS program structures and industrial structures in Tianjin, China. The industrial structure is categorized into primary, secondary, and tertiary industries. SVS program structures are evaluated using indicators including program scale (admitted, enrolled, and graduated students per industry), and program quantity (number of programs per industry). The industrial structure is measured using GDP and employment figures per industry. An entropy weighting method is employed to determine the weight of each indicator in the system. The overall evaluation index is determined using a power function, calculating the contribution value of each indicator. The coupling degree (C) is calculated using a capacity coupling coefficient model, and the coupling coordination degree (CCD, D) is calculated to avoid the illusion of high coupling with low development. A modified classification criteria for coupling coordination levels is used. Grey relational analysis is then used to explore the correlations between the indicators of SVS program structure and the CCD. Data from Tianjin's Statistical Yearbooks and SVS admission announcements are used for the period 2013-2019. Correlation analysis using Pearson's correlation coefficient is used to investigate interactions between program quantity, GDP, and employment figures per industry. This analysis is extended to include correlation between the program scale and industrial structure.

The study reveals a strong interaction between SVS program structures and the industrial structure, particularly the secondary industry. Correlation analysis shows a strong negative correlation between the number of secondary industry-related programs and the industry's GDP, but a strong positive correlation with employment in the secondary industry. For the tertiary industry, negative correlations exist between the number of programs and both GDP and employment, suggesting an oversupply of graduates in this sector. Analysis of the CCD shows that the coupling coordination between SVS program structure and industrial structure has fluctuated between good coordination and mild incoordination during the study period (2013-2019). The year 2014 witnessed the highest CCD (good coordination), attributed to a significant increase in the SVS program structure following the implementation of a skilled talent cultivation pilot project. Conversely, 2019 saw the lowest CCD (mild incoordination) due to reduced student admissions. Grey relational analysis indicates that indicators related to secondary industry programs (enrollment, admission, graduates, and number of programs) have the strongest influence on the CCD, emphasizing the importance of aligning SVE with the secondary industry's needs. Overall, the findings suggest that while the interaction between SVS program structure and the industrial structure is strong, particularly with the secondary industry, significant improvements are needed to ensure better coordination and reduce skill mismatches, especially in the primary and tertiary industries.

The findings highlight the importance of aligning SVE program structures with the dynamic needs of the industrial structure. The strong correlation between SVS programs and the secondary industry in Tianjin underscores the success of aligning education with a key economic sector. However, the study also reveals a need for strategic adjustments in primary and tertiary industry programs to avoid skill surpluses and promote graduate employment. The fluctuating CCD emphasizes the dynamic nature of the relationship and the need for ongoing monitoring and adjustments of SVE policies to address shifting industrial demands. The study's focus on Tianjin allows for a detailed analysis of the coupling coordination relationship but limits the generalizability of the findings. Future studies should consider a broader geographical scope and incorporate qualitative data to gain a more comprehensive understanding of the complexities involved.

This study provides a novel framework for measuring the coupling coordination relationship between SVS program structures and industries. The findings reveal a strong but uneven relationship, with the secondary industry showing the closest alignment. Recommendations include adjusting program numbers to match industry needs, focusing on improving primary and tertiary industry programs to strengthen graduate employability, and actively monitoring and adjusting SVE policies to adapt to dynamic industrial changes. Further research is needed to replicate this study in other regions, explore the relationship's evolution over time, and examine the driving factors behind the observed relationships.

The study's main limitation is its focus on Tianjin, China, which may not be fully representative of other regions with different industrial structures and SVE systems. The data selection may also introduce bias, as the study excludes vocational high school students and those in the 3+2-year program. Future research should expand the sample size to include more regions in China and incorporate a broader range of student populations to ensure greater generalizability.