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Manufacture of optical fibers is subject to inherent uncertainty in various process and material parameters, which, in turn, leads to variability in product quality and impacts the reliability of the optical fibers in use. Analysis of the interactive effects of parameter uncertainty on the optical fiber quality is imperative in a robust-design endeavor. To this end, a methodology for simulation of optical fiber drawing process under uncertainty is presented by considering a two-dimensional (2D) numerical model of the flow, heat and mass transfer phenomena involved in the fiber drawing process. A sampling-based stochastic model is developed, and parametric analysis is presented to elucidate the effects of uncertainty in several process and material parameters on the variability of index of refraction, residual stress, maximum tension, and defect concentration. Design maps are derived from the analysis which provide for selection of furnace wall temperature as a function of the input parameter uncertainty and target maximum acceptable variability in the index of refraction, residual stress, maximum tension, and defects.