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This paper presents a comprehensive characterization and an optimization method for clockless wave pipelines (CWP) with intra-wave and inter-wave faults. The CWP in this paper solely relies on the request signal as a primary clockless-induced control over data waves without the need for clock distribution. Delay fault models in such CWPs are proposed, in which the faults with respect to data waves and their associated request signal are theoretically identified and characterized in a comprehensive manner. The co-relation between the two fault models is revealed such that an inter-wave fault is a subset of an intra-wave fault model. A fault rate modeling and analysis is shown to conduct an optimization of fault rate and yield. A yield optimization can be conducted by finding the optimal value of the difference of propagation time of the slowest data bit of a data wave and its associated request signal in the intra-wave fault model, and by finding the optimal value of the difference of transition speed of rising bits and that of falling bits in the inter-wave fault model. The proposed optimization methods are verified through numerical simulation to demonstrate their efficiency and effectiveness with respect to yield.