00328 ¿80eb3e1366a39705d7b77d62f12780

331

Optimizing Defect Levels and Losses from Gage Errors

ao

P(good| reject) = J[2813.48e‘^{<,<XM,O78,25(zll30)2}{O.5-O.5erfl0.O353553(z-12OO)]}

1250

{05 - 0ierf[0.0471405(z-1225)] }]dz where the erflz] is the integral of the Gaussian distribution such that

Finally, the probability of a reject unit being accepted as a good unit is P(good|reject) = 1.528 E-6

which is 1.528 ppm defective units being passed on to the customer.

By utilizing EÄ…uation (14) for two gages, the probability of the gage rejecting a good unit is

e ^{2    20} dw

1 w-[200 2

After performing the integration inside the square brackets, the eÄ…uation becomes

1230

P(good|reject) = J(4986.78e^^000078,25(z'¹¹³⁰⁾² {[1 - l][05-0.5erf)0.0353553(z-1200)]}

{0.5 - 0.5erf]0.0471405(z -1225)]} ]dz

Upon completing the finał integration, the probability is

P(reject|good) = 0.136772

Although the probability of a customer receiving a defective unit is extremely Iow, the probability of throwing away a good unit by the gage is very high at