An asymmetric tolerance design occurs when deviation (from the ideal target) of a quality characteristic in one direction is more harmful than in the opposite direction. Asymmetric tolerances are common in many manufacturing processes. Traditionally, the designer of a manufactured component either would choose the smaller tolerance as the tolerance for both sides of the ideal target, or would set a process mean at the middle of the tolerances. Both methods fail to minimize the expected value of Taguchi's societal quality losses when the quality loss function is asymmetric. Linear and quadratic quality loss functions are considered to determine the optimal value of a process mean that minimizes the expected value of the quality loss function. Also, a quality loss model involving a pokayoke defect prevention procedure is investigated.