High School

Suppose that a metal rod is supposed to be cut to a length of 51.8 mm. The upper specification limit is set at 52.9 mm, and the lower specification limit is set at 50.7 mm. A metal rod that is out of specification must be scrapped at a cost of $38.00. The company uses the Taguchi Quality Loss Function to estimate quality costs.

A sample of three units was taken, and the rod measurements were 51.7 mm, 52.4 mm, and 53.3 mm, respectively. What is the total Taguchi Quality Cost of that sample of three units?

a) The Taguchi parameter \( T \) is _____

Answer :

The total cost considering the measurements provided is $82.268.

To determine the total Taguchi Quality Cost for the given sample of three units, we first need to calculate the Taguchi Loss Function for each rod. The formula for the Taguchi Loss Function (L) is:

L(y) = k(y - T)^2

where y is the measured value, T is the target value, and k is a constant determined by the cost of deviation. Given the upper specification limit (USL) of 52.9 mm, the lower specification limit (LSL) of 50.7 mm, and a scrap cost of $38.00.

Now, let's calculate the loss for each measurement:

For 51.7 mm: L(51.7) = 31.40(51.7 - 51.8)^2 = 31.40(−0.1)^2 = 31.40 \\times 0.01 = 0.314

For 52.4 mm: L(52.4) = 31.40(52.4 - 51.8)^2 = 31.40(0.6)^2 = 31.40 \\times 0.36 = 11.304

For 53.3 mm: L(53.3) = 31.40(53.3 - 51.8)^2 = 31.40(1.5)^2 = 31.40 \\times 2.25 = 70.65

Summing these values gives the total Taguchi Quality Cost:

Total Cost = 0.314 + 11.304 + 70.65 = 82.268

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