Question

The A unit filling line at Microfarmosutica, Inc., must fill of 2.5 ± 0.2 ml of eyedrop solution into each container. It costs $1.10 to scrap a defective unit. A sample of 50 containers was drawn from the production process, which has been determined to be approximately normally distributed, with: x = 2.4906; ? = 0.0057 • What is the value of k in the Taguchi loss function? • What is the expected loss per unit?

Answer 1

a)

Taguchi loss function is given by:

L(x) = k(x-T)²

Since cost per unit is $2, L(x) =$2 and (x-T) = 0.2ml.

Therefore,

2 = k(0.2)²

k=50

b)

Now,

D= 2.5 - 2.4906 = 0.0094

$\sigma^2$ = 0.0057

The expected loss is given by:

$EL = k(D^2+\sigma^2)=50(0.0094^2+0.0057)=0.289$

Therefore, the expected loss is $0.29 per unit.