Question

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 = $32,000 and T = 0.26 inches in diameter. A sample of four units produced the following values: Unit Actual Diameter No. 1 0.26 2 0.27 3 0.23 4 0.24 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 100,000 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? $

Answer 1

Please find below table useful to compute desired results: -

А B G m 1 Unit 2 1 3 2 4 3 5 4 y 0.26 10.27 0.23 0.24 C D E F y-m (y-m)2 k*(y-m)^2 0.26 =B2-C2 =D242 =E2*32000 0.26 =B3-C3 =D342 =E3*32000 0.26 =B4-C4 =D4^2 =E4*32000 0.26 =B5-C5 =D542 =E5*32000 =SUM(F2:F5) 1. Average Loss =F6/A5 Multiplier 6 6 6 H Loss =G2*F2 =G3*F3 =G4*F4 =G5 F5 6 7 3. Measured External Cost =SUM(H2:H5) 8 9 Total Units Produced 100000 10 2. Total Hidden Cost =B9*F7

End results would be as follows: -

A B с D E (y-m)^2 1 Unit у y-m 2 3 1.00 2.00 3.00 4.00 m 0.26 0.26 0.27 0.26 0.01 0.23 0.26 (0.03) 0.24 0.26 (0.02) F G H k*(y-m)^2 Multiplier Loss 6.00 3.20 6.00 19.20 28.80 6.00 172.80 12.80 6.00 76.80 44.80 11.20 3. Measured External Cost 268.80 0.0001 0.0009 0.0004 4 5 6 7 1. Average Loss 8 9 Total Units Produced 10 2. Total Hidden Cost 100.000.00 1,120,000.00