1. (21 points) Suppose that a steel blank is supposed to be pressed 7.5 mm deep as part of an automotive stamping process. The upper spec limit is set at 9.1 mm, and the lower spec limit is set at 5.9 mm. A steel blank that is out of spec must be scrapped at a cost of $125. The company uses the Taguchi Quality Loss Function to estimate quality losses. Suppose that a sample of 4 units was taken, and the depth measurements were: 7.5, 8.65, 7.1, and 5.99 mm, respectively.

a. A Quality Consultant believes that the Taguchi Quality Loss Function is an appropriate measure for quality costs. What is the Taguchi Quality Cost Function corresponding to the given specifications?

b. Calculate the total Taguchi Quality Cost the company will have to incur (if any), due to the units included in the said sample. Alternatively, the in-house Quality Assurance Manager likes the idea of a Taguchi Quality Loss Function, but believes that a linear function would better represent the cost of quality. Specifically, she prefers a loss function of the form: L=T|D|, where L, D, and T have the same definitions as in the Taguchi model (|| denotes the absolute value of . For example, |-5|=5 and |5|=5).

c. What is the Quality Cost Function corresponding to the given specifications?

d. Calculate the total Quality Cost the company will have to incur (if any), due to the units included in the said sample under the new cost function.

e. Comment on what you think is a better model to calculate quality costs of the company. (Note that there's no correct answer to this question, as it is a highly subjective matter. Providing a sound argument to show why your preferred model is better than the other would suffice)