00324 î4f0003b2ed2810dd76bb30abe464e6

327

Optimizing Defect Levels and Losses from Gage Errors

goals yet also achieve a minimum yield loss due to gage error. The next section develops the equations used for determining yield loss in single and multiple gage systems utilizing guard bands.

Gage Losses for Systems of Gages with Guard Bands

The yield loss that is a consequence of the non-optimum setting of guard bands can strongly affect productivity and even a company's ability to meet customer delivery demands. It is also very likely that thousands of dollars could be lost daily due to gage errors and the associated improperly set guard bands. By using some of the standard guard banding methods discussed earlier, an engineer would not know the losses that were being generated. Also, it would be highly unlikely that the losses would be at a minimum.

In a similar fashion to that for determining the defect levels for a single gage system with a guard band, the yield loss due to gage error can be found. Again, by using the eÄ…uality shown in Equation (7) and by integrating from negative infinity to the guard band chosen, the probability of a good unit being thrown away by the gage can be calculated as follows:

USL z

P(reject|good) = J [ f(z) J g' (y)dy ]dz    (11)

For multiple gage systems, the development of the gage loss eÄ…uations is morÄ™ compIex. Because the first gage removed good units, the second gage sees an altered product distribution. Therefore, the ppm of the good remaining in the population must be calculated prior to determining the effect of the second gage. The probability that the first gage rejects a good unit is

USL z

P(gagel rejectsjgood) = J[f(z)Jg'i (w)dw]dz

As previously mentioned, this is equivalent to the gage loss for the first gage. The probability of good units remaining in the product distribution is found as follows:

USL

USL z

P(good units remaining)

J f(z)dz - J[f(z)Jg^,,(w)dw]dz

.co    .co