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In the contemporary world of engineering, engineers strive towards designing reliable and robust artifacts while considering and attempting to control manufacturing costs. In due course they have to deal with some sort of uncertainty. Many aspects of the design are the result of properties that are defined within some tolerances, of measurements that are appropriate, and of circumstances and environmental conditions that are out of their control. This uncertainty was typically handled by using factors of safety, and resulted in designs that may have been overly conservative. Therefore, understanding and handling the uncertainties is critical in improving the design, controlling costs and optimizing the product. Since the engineers are typically trained to approach problems systematically, a stepwise procedure which handles uncertainties efficiently should be of significant benefit. This thesis revises the literature, defines some terms, then describes such a stepwise procedure, starting from identifying the sources of uncertainty, t