00325 �437d425376f31708da407e970fe43f

328

McCarvilIe & Montgomery

USL    z

= J[f(z) -f(z) Jg'i (w)dw]dz

.«0    .«0

USL    z

= J f(z) 11 - Jg'i (w)dw]dz

.00    .00

ust    «

= J f(Z) I J g'i (w)dw]dz

-flO    Z

By multiplying in the gage2 error, the losses due to gage2 can be calculated as follows:

P(gage2 rejects(good) =

USL    ®    z

Jf(z) I Jg', (w)dw][ Jg'₂ (x)dx]dz

(12)

Likewise, the yield loss caused by a third gage is

P(gage3 rejects|good) =

USL <«>    ®    z

Jf(z)lJg'i(w)dw][ Jg'₂ (x)dx][ Jg*₃ (y)dy]dz

(13)

-oo    z

The total losses for a three gage system can now be determined by summing up the losses for gagel, gage2, and gage3.

USL z

P(3 gages rejectjgood) =    J[f(z) Jg', (w)dw]dz

.ao    -oo

USL    <*>    z

+    Jf(z)    l    Jg’i    (^w)dw](    Jg’₂(x)dx]dz

-00    z    -oO

USL    oo    oo    z

⁺    J f(z)    I    |g'i(w)dw][    Jg'₂(x)dxn    Jg'₃(y)dy)dz

.00    z    Z    -00

The outside integral can be Consolidated resulting in

USL    z

P(3 gages rejectjgood) = J(f(z) [ Jg', (w)dw]