Quality-reliability chain modeling for system-reliability analysis of complex manufacturing processes

System reliability of a manufacturing process should address effects of both the manufacturing system (MS) component reliability, and the product quality. In a multi-station manufacturing process (MMP), the degradation of MS components at an upstream station can cause the deterioration of the downstream product quality. At the same time, the system component reliability can be affected by the deterioration of the incoming product quality of upstream stations. This kind of quality & reliability interaction characteristics can be observed in many manufacturing processes such as machining, assembly, and stamping. However, there is no available model to describe this complex relationship between product quality, and MS component reliability. This paper, considering the unique complex characteristics of MMP, proposes a new concept of quality & reliability chain (QR-Chain) effect to describe the complex propagation relationship of the interaction between MS component reliability, and product quality across all stations. Based on this, a general QR-chain model for MMP is proposed to integrate the product quality with the MS component reliability information for system reliability analysis. For evaluation of system reliability, both the exact analytic solution, and a simpler upper bound solution are provided. The upper bound is proved to be equal to the exact solution if the product quality does not have self-improvement, which is generally true in many MMP. Therefore, the developed QR-chain model, and its upper bound solution can be applied to many MMP.