High School

Suppose that the specifications for a part (in inches) are 6 inches, and that the Taguchi Loss Function is estimated to be [tex]L(x) = 8700(x - T)^2[/tex]. Determine the estimated loss if the quality characteristic under study takes on a value of 6.2 inches. If you make 100 parts a day and 4 are 6.2 inches, how much are you losing every 5-day work week?

A. $348, $1062
B. $1041, $34,000
C. $1360, $34,000
D. $1041, $26,025
E. $348, $6960

Answer :

The correct answer is E. $348, $6960.

The Taguchi Loss Function is used to estimate the cost associated with deviations from a target value. In this case, the target value is 6 inches and the loss function is L(x) = 8700(x - T)^2, where x is the quality characteristic value and T is the target value.
To determine the estimated loss when the quality characteristic value is 6.2 inches, we substitute x = 6.2 into the loss function:
L(6.2) = 8700(6.2 - 6)^2 = 8700(0.2)^2 = 8700(0.04) = 348.
Therefore, the estimated loss is $348.
To calculate the loss over a 5-day work week, we need to determine the number of non-conforming parts. Given that 4 out of 100 parts have a value of 6.2 inches, we can calculate the average number of non-conforming parts per day:
(4 parts / 100 parts) * 100 parts/day = 4 parts/day.
Thus, we are losing 4 parts/day.
Over a 5-day work week, the total loss would be:
4 parts/day * 5 days/week = 20 parts/week.
Since the estimated loss per part is $348, the total loss over a 5-day work week would be:
20 parts/week * $348/part = $6960.

Learn more about Taguchi Loss Function here,
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