The desired target quality characteristic of a product of Hanson Component Manufacturing is 0.5. The customer-service manager knows that customers are likely to complain when the specification is off the desired quality characteristic by more than 0.025. On average, it costs the firm $2,000 to handle and resolve each complaint. The production manager of the Hanson Manufacturing suggests that the company test the product more thoroughly before shipping. The cost of additional testing and adjustments is estimated at $30.00 per unit.

Given the company's cost coefficient, k, what should the tolerance be (to five decimal places) before conducting additional testing and adjusting at the factory?
A) 0.00001.
B) 0.00306.
C) 0.00063.
D) 0.02500.
E) 0.25000.

Question

The desired target quality characteristic of a product of Hanson Component Manufacturing is 0.5. The customer-service manager knows that customers are likely to complain when the specification is off the desired quality characteristic by more than 0.025. On average, it costs the firm $2,000 to handle and resolve each complaint. The production manager of the Hanson Manufacturing suggests that the company test the product more thoroughly before shipping. The cost of additional testing and adjustments is estimated at $30.00 per unit.

Given the company's cost coefficient, k, what should the tolerance be (to five decimal places) before conducting additional testing and adjusting at the factory?

Given the company's cost coefficient, k, what should the tolerance be (to five decimal places) before conducting additional testing and adjusting at the factory?
A) 0.00001.
B) 0.00306.
C) 0.00063.
D) 0.02500.
E) 0.25000.

Quizplus · Accepted Answer

The tolerance should be determined based on the cost-benefit analysis of additional testing versus the cost of handling complaints. The formula to calculate the optimal tolerance (δ) is given by δ = sqrt(3kC), where k is the cost of testing and adjusting per unit ($30) and C is the cost of handling a complaint ($2000). Substituting the values, we get δ = sqrt(3*30*2000) = sqrt(180000) = 0.00306.

The Desired Target Quality Characteristic of a Product of Hanson