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Optimizing Defect Levels and Losses from Gage Errors

FigurÄ™ 2. Equality Relationship for the Probability of a Defective Unit, xj, Being Measured by the Gage as a Good Unit

(3) is used. If a guard band is used, then the mean of the gage distribution becomes the guard band.

FigurÄ™ 3 shows the relationship of the probability of having a rangÄ™ of defective units, dx, and the associated probability of these defective units being accepted by the gage as good units. By integrating all of the probabilities of having reject units of product fali in dx ranges multiplied by their associated probabilities of being accepted from the specification limit to positive infinity, the defect level can be as follows:

(5)

P(good)reject) =    J [f(z)J g' (y)dy ]dz

USL i

Although the focus so far has been on the probability or risk of sending defective units to the customer or further along the assembly linÄ™, it would certainly be of interest to minimize the probability of throwing away a good unit. The probability of discarding a good unit, xj is: