Supply chain is the operation of the flow of goods and services, and includes all processes that transform raw materials into final products. It involves the active streamlining of a business's supply-side activities to maximize customer value and gain a competitive advantage in the marketplace. In recent years, many researchers have proposed the integrated supply chain models with production, inspection, maintenance and quality. Chuang and Wu (2019) developed an integrated model to determine the optimum supplier’s process mean and quality investment settings and retailer’s number of shipment, order quantity and maximum backorder quantity with maximization of total profit of supply chain system. In the present paper, Chuang and Wu’s model is modified with the constraint of the specified process capability index Cpm value, where the mean and standard deviation of process characteristic are assumed to be the declining exponential reduction function. The decision variables in this modified model include supplier’s parameters (i.e., quality investment and specification limits) and retailer’s parameters (i.e., order quantity, number of shipments and maximum backorder quantity). A numerical example is provided for illustration. Based on the sensitivity analysis, it may be seen that the supply chain’s total profit is positively influenced by the production rate, the demand rate, the purchasing cost, the selling price and the quality investment, and is negatively affected by the production cost, the specified process capability index, the target value, the maximum mean and both the minimum and the maximum standard deviations of process characteristic.