Question

A quality characteristic has a specification (in inches) of 0.100 = 0.020. If the value of the quality characteristic exceeds 0.100 by the tolerance of 0.020 on either side, the product will require a repair of $230. Develop the appropriate Taguchi loss function. Round your answer for the first field to the nearest whole number and the answer for the second field to three decimal places. .)Calculate the k value corresponding to the Taguchi loss function. Round your answer to the nearest whole number. k=

Answer 1

The appropriate Taguchi loss function is developed using the given quality characteristic specification and repair cost, yielding a proportionality constant k value of 575000, which illustrates the Taguchi philosophy of minimizing variance from the target to lower societal costs.

Step-by-step explanation:

The student's question revolves around developing a Taguchi loss function based on a given quality characteristic specification for a product. The taguchi loss function formula is given as L(y) = k(y-T)², where T is the target value, y is the actual value, and k is a proportionality constant. Since the specification is 0.100 ± 0.020 inches, T is 0.100. When y exceeds the tolerance, a repair cost of $230 is required. We can solve for the k value by substituting the tolerance limit and repair cost into the formula which gives k = Loss / (Specification deviation)². The repair cost associated with the deviation of 0.020 inches is $230, therefore k = 230 / (0.020²) = 230 / 0.0004 = 575000.

Taguchi's philosophy is to minimize the variance from the target as this will lead to lower costs for society. By using the Taguchi method, businesses can ensure they minimize variance while also meeting quality standards, resulting in a cost-effective and efficient production process.