00332 ž133d2464eb28601d2d991683b45647

335

Optimizing Defect Levels and Losses from Gage Errors

on the details of building response surface models, see Montgomery (199la) and Box and Draper (1987). For the ppm(Def) response, we found that a fuli Ä…uadratic response surface model on the natural log scalÄ™ was adequate. Using the coded variables Xi and X2, the model is

Ln(ppm(Def)) = 5.122 + 0.775Xi + 1.483X2

-    0.098Xi² - 0.224X2² + 0.012XiX2    (15)

The model can be transformed into the natural variables GB1 and GB2 as follows:

Ln(ppm(Def) ) = -627.484 + 0.56136(GB1) + 1.3125(GB2)

-    4.338E-4(GB1)² - 9.969E-4(GB2)²

+ 5.208E-5 (GB 1 )(GB2)    (16)

FigurÄ™ 12 is the contour plot of the Ln(ppm(Def)). As expected, the defective level increases as the guard band settings for the gages are decreased. FigurÄ™ 13 is the three dimensional representation of the ppm(Def) response on the original units.

A Ä…uadratic model was also used for the natural log of the gage loss response. In terms of the coded variables, the model is

Ln(Gage Loss) = 11.1968 - 0.2306Xi - 0.2062X2

+ 0.0197Xi² + 0.0267X2² - 0.1003XiX2    (17)

The model can be transformed into the natural variables as follows:

Ln(Gage Loss)= -64.3425 + 0.15403(GB1) + 0.11682(GB2)

+ 8.743E-5(GB1)² + 1.185E-4(GB2)²

- 4.459E-4(GB1)(GB2)    (18)

The contour and three dimensional plots for the Gage Loss model are shown in Figures 14 and 15. The contour plot is shown with the natural log transformation while the three-dimensional plot is on the original natural units. Contrary to the ppm(Def) model, the Gage Loss increases as the guard bands are decreased.