00313 N8ca2ce47ae6338a7cbe578cf96f640

316

McCaryille & Montgomery

Figurę 1. Probabiiity of xj,, a Reject Unit, Being Measured by the Gage as

a Good Unit

The proof of this relationship can be seen graphically by comparing the standard normal values. Notę that z' is the negative of z.

Xj - USL _ -(USL - x;)    _    ,

This equality makes the calculation of the probabiiity of having a defective unit accepted by the gage as a good unit much easier. The eąuality in Eąuation (3) is easily seen in Figurę 2.

By using the eąuality shown in Eąuation (3), we will show that the defect level can be calculated given that g(y) is normally distributed with a mean eąual to the upper specification limit and a standard deviation eąual to the standard deviation of the gage. By doing this, the mean of the gage distribution remains the specification limit while the starting point of the integration increases as the value of xj increases for the product. If the left side of Eąuation (3) was used, then the mean of the gage would vary with the xj of the product. The calculation is madę easier by maintaining the same distribution throughout the calculation, and therefore, the right side of Eąuation