5. Taguchi (1987) described an experiment to nd the source of clutch slip-

ping in automobiles. Prototype clutches were assembled using some new components and some components taken from disassembled clutches that had complaints. Each prototype was tested and the response, y, was ob-

tained by dividing the slipping time by the number of revolutions of the engine and then multiplying by 10,000. The control and noise factors and their levels are shown in Table 12.21.

A 20-run orthogonal array (shown in Table 12.22) was used to study both control and noise factors in a single array.

(a) Read the data into a SAS data set and construct ????1 and +1 coded factor levels for factors A, D, F, C and 4 orthogonal polynomial contrasts for factor B. Create columns for the interactions between control and noise factors.

(b) Find a model for the data using an all-subsets regression, as shown for analysis of a Plackett-Burman design in Section 6.6 and for the analysis of the log variance for the temperature controller circuit in Section 12.4.

(c) From your model, identify any signicant adjustment factors and control-
by-noise interactions, and determine the levels of the control factors that will minimize clutch slippage with minimum variation.

(d) Are all control-by-noise factor interactions estimable from this design?
If not, construct an orthogonal-array design or orthogonal main-eect plan that allows estimation of all control by noise interactions by using the interact= option of the %mktex macro as shown in Section 6.7.

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Table 12.21 Factors and Levels for Auto Clutch Slipping Levels Control Factors: + B:Spring Allignment 5 levels A:Force current +50kg D:Clutch Plate Running Distance 10,000km 30,000km F:Cover Running Distance <10,000km >30,000km Levels Noise Factors: + C:Clutch Plate ordinary product object of complaint E:Cover ordinary product object of complaint