Problem set 3 2023
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CHEME 5610: Product Design/Lean Operations Design
Problem Set #3 (50 Points): Assigned September 14, 2023
Due: September 28, 2023
Your customer from the Robust Design Contest has also contracted your company to help them
understand their manufacturing tolerances for their soup base product.
As you know, the desired drain
time through a #4 Ford viscometer cup for this product is 13.6 seconds. Feedback from potential
customers indicates if the drain time from a jar is greater than 15.2 seconds or less than
12 seconds, then half of the customers will discard the entire jar and go to the store to purchase a
replacement at the full retail price.
The target retail selling price for each one-liter jar of the soup base in a supermarket is $6.99. Of course,
some of that price includes the company’s profit. The manufacturing cost for each jar is only $2.20. The
company plans on selling jars of the soup base to supermarkets for $5.38 each. To make a profit on each
sale, supermarkets will sell each jar for 30% more than they pay for it, or $6.99.
The drain time through a #4 Ford viscometer cup is measured in the factory for each batch of soup base. If
the drain time is too low, additional gum can be added to the batch to make the soup base more viscous. If
the drain time is too high, the batch can be diluted with additional water to reduce the drain time. In both
cases, the manufacturer will incur a cost of $0.48 per one-liter jar to rework a batch of soup base. This cost
includes the additional ingredients, labor, and reduced throughput of the factory.
1.
(20 points)
Use the above information to determine the equation for Taguchi's Quality Loss Function
(
L
) for this manufacturer and this product. Please be sure to specify the units of every term in your
equation.
2.
(20 points)
Use the quality loss function you determined in question #1 to set the manufacturing
tolerances for this product. In other words, at what value of drain time should the manufacturer spend $0.48
(per one-liter jar) to rework a batch of the soup base?
3.
(10 point)
Suppose a jar of soup base with a drain time of 15.4 seconds is shipped. What is the
financial loss to society? How would this loss become apparent to the manufacturer
?
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