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In engineering design and manufacturing optimization, the trade-off between a quality performance metric and the probability of satisfying all performance specifications (yield) of a product naturally leads to a chance-constrained bi-objective stochastic optimization problem (CBSOP). A new method, called MOOLP (multi-objective uncertain optimization with ordinal optimization (OO)), Latin supercube sampling and parallel computation), is proposed in this paper for dealing with the CBSOP. This proposed method consists of a constraint satisfaction phase and an objective optimization phase. In its constraint satisfaction phase, by using the OO technique, an adequate number of samples are allocated to promising solutions, and the number of unnecessary MC simulations for noncritical solutions can be reduced. This can achieve more than five times speed enhancement compared to the application of using an equal number of samples for each candidate solution. In its MOEA/D-based objective optimization phase, by using LSS, more than five times speed enhancement can be achieved with the same estimation accuracy compared to primitive MC simulation. Parallel computation is also used for speedup. A real-world problem of the bi-objective variation-aware sizing for an analog integrated circuit is used in this paper as a practical application. The experiments clearly demonstrate the advantages of MOOLP.