00326 A9b69718dd18cd338e0f0700b7c79c2

00326 A9b69718dd18cd338e0f0700b7c79c2



329


Optimizing Defect Levels and Losses from Gage Errors

+ f(z)[ jy,(w)dw][ Jg’2(x)dx]

z    -«o

oo    oo    z

+ f(z)[ Jg', (w)dw][ Jg'2 (x)dx] [ Jg'3(y)dy]}dz

Z    z    -00

Knowing that the integraJ of a density function from negative infinity to z is equal to one minus the integral of the density function from z to positive infinity, along with extracting f(z) from the gage components, results in

USL    *

P(3 gages rejectjgood) =


Expanding shows P(3 gages rejectjgood) =


Jf(z) {[ 1 - |g',(w)dw]

-00    z

00    «0

+ 1 Jg'i (w)dw][l - Jg*2 (x)dx]

Z    z

+ f Jg'i(w)dwH Jg*2(x)dx][1 - Jg'3(y)dy]}dz

z    z    z

USL    «    *

Jf(z) {1- Jg', (w)dw+ Jg', (w)dw

ao    00    00    00

-    Jg'i (w)dwjg'2 (x)dx + Jg'i (w)dwjg'2 (x)dx

Z    Z    Z    Z

QO    00    00

-    Jg'i (w)dwjg'2 (x)dxjg'3 (y)dy}dz

Z    Z    Z

By removing the like terms, this reduces to

P(3 gages rejectjgood) =

USL    ®    =o    oo

(14)


Jf(z) {1- Jg'i (w)dwjg'2 (x)dxJg'3 (y)dy}dz

-oo    z    Z    Z

A logie check can be performed by subtracting the good units saved after the gages have been used from the total good units in the population. The eąuation for the good units saved is:


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