This paper studies an assembly system consisting of multiple upstream complementary suppliers and a single downstream assembler, where quality improvements in the components made by the suppliers have positive externalities. Specifically, the demand of final products can be enhanced by improving the quality of components. The complementary component suppliers can freely form coalitions to determine their wholesale pricing and quality-improvement efforts. Based on the concept of Nash stability, this paper characterizes the stable coalition structure of suppliers and the equilibrium decisions of the assembly system, and further discusses the influence of positive externalities of supplier quality improvement on the system. The results show that a grand coalition forms when the overall quality improvement efficiency of suppliers is high; otherwise, the suppliers act independently. In addition, due to the positive externalities of supplier quality improvement, suppliers with low quality-improvement efficiency can benefit from free riding. Compared to suppliers with higher quality-improvement efficiency, they make less effort in quality improvement but obtain higher profits. Finally, the free-riding behavior of suppliers is illustrated through numerical examples.