Companies are under increased pressure to manufacture products that have a high level of quality. Manufacturing products with a high level of quality in a cost-effective manner requires the products to be designed so that they can be manufactured with an acceptable level of variation. Creating a new design that can be produced with the necessary level of variation has historically been a very challenging problem. A new method for calculating the effect a manufacturing process has on the mean and standard deviation of a distribution is presented. This new method is founded on the concept of characterizing a manufacturing process with two math functions called DeltaP and SigmaP. DeltaP and SigmaP represent the theory of Process Imparted Dimensional Change and Process Imparted Variation. Using these functions, closed-form solutions for the mean and standard deviation of a distribution exiting a manufacturing process can be calculated. The authors present the background of the theory as well as the derivation of the closed form solutions for the output mean and standard deviation from a generic manufacturing process. The derivation is followed by a simple example to demonstrate the method.

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