Vehicle transmission repairs for part number TAC45123 are costly to replace. A highly skilled mechanic must disassemble the transmission. If the part fails while it is in warranty, the manufacturer pays the full cost of the repair to the garage or dealer that did the repair. The manufacturer uses the Taguchi loss function to set a specification for the part with k = 40,000. The dimensions for the part are 1.0 ± 0.10 centimeters.

a. What is the economic value of one failed part?

b. If the manufacturer of the part paid the full warranty cost on 1,862 failures last year worldwide, what is the total economic cost of failure?

c. If the manufacturer improved process and equipment capability so the part specifications changed to 1.0 ± 0.05 centimeters, what is the economic cost of one failure?

d. Assuming failures were reduced by one half to 931 due to the more precise specifications, what is the economic cost of failure?

e. How much warranty cost is saved according to Taguchi estimates by improving specifications from ± 0.10 to ±0.05?