Taguchi Loss Function

a. An automobile parts manufacturing company produces a certain part with most critical dimension as 40.50 ±0.025 in (specifications). If the manufacturing process produces some parts whose tolerance is exceeded then these specifications, then customer will return the part to the manufacturer for a replacement new part which will cost the company a cost of $250 in rework and replacement expenses. (a.1) Determine the constant k in the Taguchi loss function, (Text book Eq. (37.13). (a.1) The company can add a finishing grinding operation that will to reduce the tolerances to ±0.010 in. Using the Taguchi Loss Function from part (a.2) what is the value of the loss associated with this new tolerance?

b. The fine grinding operation introduced in the manufacturing process will add $2.50 to the current cost of the part, which is $15.50. If the returned parts for replacement from the customer at the tolerance of ±0.025 in is 2.5%, and it is expected to drop to zero returns if the new tolerance of ±0.010 are realized, is it economically justified to add the finish grinding operation to the manufacturing sequence for the part? Answer this question using the basic cost and returns/replacements percentage data without consideration of the Taguchi loss function.