Taguchi Loss Function
Stahman, Inc., estimates its hidden external failure costs using the Taguchi loss function. Stahlman produces plastic sheets that vary in thickness and grade. For one of its large-volume products, it was determined that k = $40,000 and T = 0.29 inches in diameter. A sample of four units produced the following values:
Unit No. | Actual Diameter (y) |
1 | 0.29 |
2 | 0.31 |
3 | 0.27 |
4 | 0.30 |
Required:
1. Calculate the average loss per unit. Round
your intermediate calculations to six decimal places. If required,
round your answer to the nearest cent and use the same in
subsequent requirements.
$ per unit
2. Assuming that 140,000 units were produced, what is the total hidden cost?
$
3. Assume that the multiplier for Stahman’s hidden external failure costs is six. What are the measured external costs?
$
PART 1
Unit | Actual Diamter(y) | m | y-m |
( y - m ) ^{2} |
Loss = k * ( y - m ) ^{2} |
1 | 0.29 | 0.29 | 0 | 0 | 0 |
2 | 0.31 | 0.29 | 0.02 | 0.0004 | 16 |
3 | 0.27 | 0.29 | -0.02 | 0.0004 | 16 |
4 | 0.30 | 0.29 | -0.01 | 0.0001 | 4 |
Total Loss | $ 36 | ||||
Avg Loss | $ 9 |
PART 2
Total units produced = 140000
So, total hidden cost = 140000 x $9 = $ 1260000
PART 3
Unit | Actual Diamter(y) | m | y-m |
( y - m ) ^{2} |
Multiplier | Loss = Multiplier * k * ( y - m ) ^{2} |
1 | 0.29 | 0.29 | 0 | 0 | 6 | 0 |
2 | 0.31 | 0.29 | 0.02 | 0.0004 | 6 | 96 |
3 | 0.27 | 0.29 | -0.02 | 0.0004 | 6 | 96 |
4 | 0.30 | 0.29 | -0.01 | 0.0001 | 6 | 24 |
Measured External Cost | $ 216 |
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