00327 271125d41fcbd8d7859983e972a0b77

330

McCarville & Montgomery

P(good|good) = J{f(z> Jg', (w)dwjg'₂ (x)dxjg'₃ (y)dy}dz while the total good units in the population is

USL

P(a unit is good) = J f(z)dz

Finally, the subtraction is

USL

USL

00

P(3 gages reject(good) =    | f(z)dz - j{f(z) Jg', (w)dwjg'₂ (x)dx Jg’₃ (y)dy}dz

.00

and this reduces to Eąuation (14) as follows:

USL

P(3 gages reject(good) = J f(z) {1 - Jg', (w)dwjg'₂ (x)dx|g'₃ (y)dy}dz

A Simple Example

Another gage is added to the previous example. The new gage has a standard deviation of fifteen. Guard bands are utilized such that the first gage is guard banded at 1200 and the second gage is guard banded at 1225.

When the product characteristic as well as the gage errors are normally distributed, Eąuation (9) becomes

dw

z^25 ₂

After performing the integration inside the square brackets, the eąuation becomes: