Heat treating is often used to carbonize metal parts, such as gears. The thickness of the carbonized layer is a critical output variable from this process, and it is usually measured by performing a carbon analysis on the gear pitch (the top of the gear tooth). Six factors were studied in a 472 design: A = furnace temperature. B = cycle time, C = carbon concentration, D = duration of the carbonizing cycle, E = carbon concentration of the diffuse cycle, and F = duration of the diffuse cycle. The experiment is shown below:

 

(a) Estimate the factor effects and plot them on a normal probability plot. Select a tentative model.

(b) Perform appropriate statistical tests on the model.

(c) Analyze the residuals and comment on model adequacy.

(d) Interpret the results of this experiment. Assume that a layer thickness of between 140 and 160 is desirable.

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Standard Order Run Order А В С D E A F Pitch 1 5 74 7 190 3 8 133 4 127 5 10 115 6. 12 101 7 16 54 8 1 144 9 6. 121 10 9. 188 11 14 135 12 13 170 13 11 126 14 3 175 15 15 126 16 4 193 I| + + + + I I + +I1 I + + I + +I + I| +I + +I + I|+ A|II IIIII + + + + + + + + UIII I + + + + I | + + + + I | + + I + + II + + I I + + +I +1+I +I+ I +I + 2.