The Taguchi loss function

Suppose we wish to determine the tolerances to be used on the length of a fluorescent electric light fitting. If the new light fitting purchased cannot be successfully installed because the length is outside tolerance, the consumer will need to return it to the supplier and suffer the inconvenience of being in the dark in the meantime. Suppose the travelling cost is £20, the value of the time lost £20 and the inconvenience a further £10 in the average case, resulting in a total cost of £50 for the consumer.
(a) Taguchi loss function is very useful for quality engineering, including tolerance design. Describe what is meant by Taguchi loss function. Discuss their three common types, applications and advantages in quality management.
(b) Assume the tolerance for the consumer 1 mm and the cost to the supplier of rectifying the situation is £2, what should be the supplier’s tolerance?
(c) If the cost of rectifying the problem by rework or making another at the manufacturer’s site is £0.50, what is the manufacturer’s tolerance?