Abstract: The efficient coordination between one risk neutral supplier and one risk neutral buyer was studied in view of products' quality failure.To maximize the profits of the bi-level supply chain,the proper quality costs of the supplier and the proper appraisal costs of the buyer were determined by the optimization method.Then,combined with the practical operation of supply chain,three kinds of utility models in accordance with how to undertake external and internal quality failure between two members were proposed and analyzed.The results indicate that,by determining the proper external partition coefficient and internal partition coefficient,the global optimization of suplpy chain and the local optimization of each member can be obtained concurrently.The conclusions are significant to guide the contract-making between members in the supply chain.

Key words: supply chain, asymmetric information, quality failure, Nash equilibrium, utility model